Giovanni Bellettini

Data di nascita: 10/30/1963

Citta': Bologna, Italia

Cittadino: Italiano

Sposato

- Data: 11/21/1988, Laurea in Matematica: (110/110 cum laude), Universita' di Pisa, relatore: Prof. Luciano

Modica

- Data: 10/28/1993. Ph.D. in Functional Analysis and Applications, presso la SISSA di Trieste, supervisor:

Prof. Gianni Dal Maso

posizione attuale (Novembre 1, 2001-)

Professore Ordinario di Analisi Matematica

Associato agli INFN, Laboratori Nazionali di Frascati (Roma), Ottobre 1, 2004-

ICTP consultant, Gennaio 1, 2012 - Agosto 31, 2012. Gennaio 1, 2013 - Agosto 31, 2013.

Membro esterno della  Commissione  per la Doctoral School in Applied Mathematics presso la SISSA

Membro di Comitato di Redazione di Interfaces Free Boundaries

1. Attivita' di ricerca

- Calculus of Variations: minimal surfaces, surfaces with prescribed mean curvature and their variational and numerical approximations, higher codimensional minimal surfaces.

Higher order problems, the elastica functional. Phase transitions and Gamma-convergence. Applications to Image Segmentation. Referenze labelled con CV (Calculus of Variations): [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [14], [15], [16], [17], [21], [23], [25], [27], [28], [33], [34], [39], [46], [47], [49], [53], [54], [56], [58], [60], [61], [62], [63], [65], [72], [74], [76], [80], [81], [83], [87], [89], [94], [105], [116], [131].

- Geometric evolution problems: mean curvature flow, weak solutions. Barriers, minimizing movements, higher order approximations. Anisotropic and crystalline mean curvature flow. The total variation flow. Referenze labelled con  GEP (Geometric Evolution Problems):

[13], [19], [22], [24], [26], [29], [30], [31], [32], [35], [36], [37], [38], [40], [41], [43], [44], [45], [48], [49], [50], [51], [52], [54], [55], [57], [66], [67], [69][70], [71], [75], [86], [90], [92], [93], [98], 100], [114], [132].

- Backward-forward parabolic equations: gradient flows of nonconvex functionals in dimension one. Weak solutions, fourth-order approximations, discretizations. Referenze labelled con BFPE (Bacwkward-Forward Differential Equations): [68], [76], [77], [78], [85], [88], [97], [103], [107], [128], [127], [129].

- Nonlinear hyperbolic equations: scalar conservation laws. The nonlinear wave equation of Ginzburg-Landau type. Referencze  labelled con  HPDE (Hyperbolic Partial Differential

Equations): [99],  [101], [111], [110], [113].

- Numerical Analysis: finite differences and finite elements approximations of parabolic partial differential equations. Discrete Gamma-convergence. Referenze labelled con NA (Numerical Analysis): [1], [4], [5], [7], [9], [17], [20].

- Statistical Mechanics: nonlocal functionals in phase transitions, nonlocal parabolic equations. Referenze labelled con SM (Statistical Mechanics): [25], [27], [51], [73], [74], [84], [91].

- Miscellanea: regularization of the two-body problem, Differential Geometry, topological problems in Computer Vision (apparent contours and their invariants, applications of singularity theory). General Relativity. References labelled by M (Miscellaneous): [40], [42], [59], [64], [79], [?], [86], [93], [98], [102], [101], [108], [109], [121], [122]. [130].

2. Attivita' seminariale

Seminari tenuti in universita' e centri di ricerca

In Italia: University of Trento (1989, 1995, 2002, 2006), University of Milano (1993, 1997), University of Roma “Tor Vergata” (1994, 1997, 1999), University of Roma “La Sapienza” (1994, 1999, 2002, 2005), University of Firenze (1996), University of l’Aquila (1996, 1997, 2004, 2007), Istituto per le Applicazioni del Calcolo, Roma (1999), University of Napoli (2000), University of Padova (2002), University of Bologna (2003), University of Trieste (2009), University of Pavia (2009), University of Udine (2009), University of Brescia (2010), ICTP (2011).

All'estero: Newton Institute, Cambridge (1995), University of Montpellier II (1996), University of Base (1997), Institute Henry Poincar`e, Centre Emile Borel, Paris (1998), Echole Polytecnique Federale de Lausanne (2003), Max Planck Institute in the Sciences, ETH Z¨urich (2004), Leipzig (2005), Universit of Pisa (2006), Max Planck Institute for Gravitational Physics, Golm (2006), University of Z¨uric (2007), University of Freiburg (2008), Hausdorff Center, University of Bonn (2008), Max Planc Institute in the Sciences, Leipzig (2010), Echole Polytechnique, Paris (2012).

speaker invitato at meetings

In Italia: Trento (1990, 1991, 1992, 1993, 1994, 1996, 1999), Catania (1991), Padova (1992, 1995) Perugia (1993), Bologna (1994), Firenze (1994), Montecatini Terme (1995), Pavia (1996), Pisa (1996, 2002), Cortona (1997, 1998, 2000), Capri (1997), Scuola Normale Superiore, Pisa (1997, 2001, 2003, 2006(2), 2008, 2009, 2010, 2012), Isola d’Elba (1997), Roma (1999, 2000, 2003, 2006, 2010 (Indam)), Levico Terme (2000, 2003, 2004, 2006, 2008, 2009, 2011, 2013), Ischia (2000), L’Aquila (2002), Lecce (2003, 2004), SISSA, Trieste (2008), Vulcano (2012). 

All'estero: Pont ´a Mousson, Metz (1991, 1994), Oberwolfach (1994, 1998, 2000, 2001, 2004(2), 2006, 2007(2), 2008, 2010, 2011 (2), 2013), Berlin (1996), Freiburg (1998), Barcellona (2000), Paris (2000), Debrecen (2003), Edinburgh (2005), Lyon (2005), Roscoff (2007), Bedlewo (2007), Z¨urich (2007), Hausdorff Center, Bonn (2008), Max Planck Institute, Leipzig (2008), Carnegie Mellon Univ., Pittsburg PA, USA (2009), Poros, Greece (2009), Max Planck Institute Golm, Germay (2009), Paris XI (2010), Dortmund, Germany (2011), Tuebingen, Germany (2011), Banach Center, Warsaw, Poland (2012), Chiemsee, Germany (2012), Athens, Greece (2012).

3. Visiting Professor

University of Maryland (United States), University of Montpellier II (France), Newton Institute (University of Cambridge, United Kingdom), University of Basel (Switzer- land), University of Ciudad Real (Spain), University of Toulon-Du Var (France), Max Planck Institute in the Sciences (Leipzig, Germany), Max Planck Insitute for Gravitational Physics (Albert Einstein Institute, Golm, Germany), University of Zuric (Switzerland), Cern (Geneve, Switzerland), Hausdorff Center (University of Bonn, Ger many), University Pompeu Fabra (Barcelona, Spain), Stockholm, KTH (Sweden).

4. Attivita' di supervisore

Studenti di laurea:

Masala M.: Sulla funzione distanza al quadrato da una variet`a, Rome 2004.

Rossi R.: A variational model for cracking in one-dimensional elasticity, Rome 2004.

Doronzo M.: Applications of Feynman-Kac formulas, Rome 2005.

Bosco A.: Simulation and experimental tests of the thermo-optical and mechanical properties of the LARES satellite for a precise measurement of the Lense-Thirring effect in General Relativity, Rome 2005.

Palandra A.: Probability and Finance, Rome 2006.

Senatore M.: Theoretical study and analysis of the thermal perturbations for the measurement of the Lense-Thirring effect with Lageos satellites, Rome 2007.

Paoli D.: Theoretical study and analysis of the thermal perturbations for the measurement of the Lense-Thirring effect with Lares satellites, Rome 2007.

Biasutto S.A.: Some economics applications of Calculus if Variations in one dimension, Rome 2007.

Caselli F.: Gamma-convergence and the least squares method: applications to differential equations, Rome 2008.

Gentile, S.: Optical characterization of the NASA LAGEOS ”sector” and the relationships with the de Sitter effect in General Relativity, Rome 2008.

Gagliardi, D.: Equazioni di Hamilton-Jacobi e applicazioni, Rome 2008.

Palandra, L. : Accurate software modeling of the GNSS laser retroreflector array characterized at the SCF-LAB for the Etrusco-2 ASI-INFN project, Degree in Engineering, Univ. Rome Tor Vergata, 2013.

ICTP Diploma students

Nguyen Thuong Ngoc Quoc: Reaction-diffusion approximations of mean curvature flow, ICTP Trieste, 2011.

Yaptieu Djengue Odette Sylvia: On some properties of mean curvature flow with forcing a pressure term, ICTP Trieste, 2011.

Ngouanfo Fopa Edith Laure: Introduction to mathematical optimal control theory, ICTP Trieste, 2012.

Abdoul Aziz Gueye Dabakh: Some topics on ordinary differential equations in mechanics and geometry, ICTP Trieste, 2012.

Mohammad Khosravi: Minimizing movements for differential equations, ICTP Trieste, 2012.

Issa Tahir Bachar: A recent variational approach to semilinear wave equations, ICTP Trieste, 2012.

Ph.D. students

L. Mugnai: Relaxation and variational approximation of curvature-dependent functionals in two dimensions, Pisa 2003.

G. Riey: Partition energies: approximation and first variation, Rome 2004.

M. Chermisi: Crystalline flows of planar networks and a geometric approach for systems of PDEs, Rome 2006.

C. Tornese: Convergence of discrete schemes for the Perona-Malik equation, Rome 2008.

L. Tealdi: title do be decided.

S. Amato: title to be decided.

5. Attivita' didattica avanzata

Some aspects of motion by mean curvature I, II, III, IV, Crete (Greece), 1998.

Geometric Evolution Problems, Minicorsi di Analisi Matematica, Padova 2003.

Anisotropic and crystalline mean curvature flow, Rome 2004.

Variational principles for geometric evolutions I, II, KTH, Stockholm (Sweden), 2007.

An introduction to mean curvature flow I, II, III, IV, University of Castilla La Mancha (Spain), 2008.

An introduction to mean curvature flow, University of Trieste (Italy), 2009.

Soluzioni deboli del flusso per curvatura media: barriere minime, SISSA (Trieste), Italy, 2009.

An introduction to mean curvature flow I, II, III, IV, Centro De Giorgi, Scuola Normale Superiore di Pisa, Pisa 2009.

An introduction to anisotropic and crystalline mean curvature flow I, II, III, IV: tutorial course, Hokkaido University,

Hokkaido, Sapporo (Japan), 2010.

Functional Analysis and Partial Differential Equations, ICTP Trieste 2011.

Partial Differential Equations and Functional Analysis, ICTP Trieste 2012.

Mean curvature flow and singular perturbations I, II, III, in Winter School on “Geometric Evolution Equations and

Related Topics”, Regensburg, October 8-10, 2012.

Corsi di dottorato

Geometric evolutions of manifolds, motion by mean curvature, Pisa 1998.

Partial Differential Equations, Rome 1999.

Calculus of Variation in one dimension: classical theory, Rome 2000.

Motion by mean curvature, Rome 2000.

Geometric Measure Theory, Rome 2001.

Calculus of Variations, Rome 2002.

Minimizing Movements, Rome 2003.

Una introduzione alle equazioni differenziali, INDAM, Rome 2005.

Anisotropic evolution problems, Rome 2006

Mean curvature flow and singular perturbations, SISSA (Trieste), 2012.

Attivita' didattica ordinaria: Analisi Matematica I e II,

Equazioni Differenziali e Analisi Funzionale

6. Organizzazione

Research projects:

- Italian coordinator of the bilateral project “Calculus of Variations: semicontinuity, relaxation, optimal design and approximation”, Italia-Spagna.

- Coordinator of the Gnampa project “ Energie anisotrope, policristalline e di partizioni, e loro evoluzione secondo la massima discesa”, Rome 2003.

- Coordinator of the Gnampa project entitled “Evoluzioni di interfacce e loro regolarizzazione mediante equazioni del quarto ordine”, Rome 2004.

- Coordinator of a research group (2004 -) at the Centro De Giorgi (Scuola Normale Superiore, Pisa) on the subject “Interface Evolutions”. Other components: V. Caselles (Barcellona) and M. Novaga (Padova).

Conferenze e workshops:

- Organizer of the workshop “Variational Problems with Free Interfaces”, Pisa, 1997.

- Organizer of the workshop “Interface Evolutions and Applications”, Centro De Giorgi, Scuola Normale Superiore, Pisa, 2004.

- Organizer of the workshop “Gradient flows of nonconvex functionals and related topics”, Centro De Giorgi, Scuola Normale Superiore, Pisa, 2005.

- Organizer of the ”Second School on Analysis and Applied Mathematics”, Univ. Roma La Sapienza, 2005.

- Organizer of the ”One day workshop on geometric evolution problems’, Centro De Giorgi, Scuola Normale Superiore, Pisa, 2005.

- Organizer of the workshop ”Recent advances on the Perona-Malik equation”, Centro De Giorgi, Scuola Normale Superiore, Pisa, 2006.

- Organizer of the workshop ”Geometric Evolutions and Applications”, Centro De Giorgi, Scuola Normale Superiore, Pisa, 2006.

- Member of the Organizing Committee of the workshop on “Nonlocal and abstract parabolic equations and their applications” Bedlewo (Poland), Banach Center, Polish Academy of Science, 2007.

- Organizer of the workshop “Geometric Evolutions and Minimal Surfaces in Lorentzian Manifolds”, Centro De Giorgi, Scuola Normale Superiore, Pisa, 2010. September 7-10, 2010.

- Co-organizer of the focus session ”Singular Geometric Evolutions of Free Boundaries”, at the Free Boundary Problem 2012 Conference, june 11-15 Chiemsee, Germany.

7. Attivita' di referaggio

Referee per le seguenti riviste: Adv. Calc. Var., Annali Mat. Pura Appl., Annali Sc. Norm. Sup. Pisa, Arch. Ration. Mech. Anal., Atti Accad. dei Lincei, Bull. London Math. Soc., Calc. Var. Partial Differential Equations, Comm. Cont. Math., Comm. Math. Phys., Comm. Partial Differential Equations, Comm. Pure Appl. Anal., Discrete Cont. Dyn. Systems, Electronic J. Differential Equations, Esaim: Control, Opt. and Calc. Var., Interfaces Free Bound., J. Comp. Phys., J. Control, Opt. Calculus of Variations, J. Convex Anal., J. Differential Equations, J. Differential Geom., J. Evolution Equations, J. Geom. Anal., J. Reine Angew. Math., Manuscripta Math., Math. Ann., Math. Meth. Appl. Sci., Meth. Appl. Anal., Pacific J. Math., Phys. A, Rendiconti Mat. Appl., Rendiconti Univ. Padova, Revista Mat. Iberoamericana, Siam J. Imaging Sci., Siam J. Math. Anal., Transactions Amer. Math. Soc

2003: referee for the Swedish Research Council.

2004: referee for the award of a Senior Fellowship of the Croucher Foundation (Hong Kong).

2007: membro di commissione per un posto a professore ordinario

2008: referee for a Ph.D. thesis at the Univ. de Bretagne Occidentale (France).

2009: member of the Committee for the evaluation of a Ph.D. Thesis at the Lab. J. Kuntzmann,

Math´ematiques Appliqu´ees-Informatique, Univ. de Grenoble (France).

2010: membro di commissione per un posto a professore ordinario

2011: member of a Committee for an associate professorship at Georgetown University (Usa).

2011: membro di commissione per un posto a professore associato

2011: member of the Commette for assigning the positions for the LaureaMagistrale at SISSA (Trieste)

2011: referee for a Ph.D. Thesis at the Universi´e Pierre et Marie Curie, Paris

Articoli di ricerca

[1] G. Bellettini: An almost everywhere regularity result for minimal partitions. Boll. Un. Mat. Ital.B (7), 4A (1990), 57–63. CV

[2] S. Baldo, G. Bellettini: ??-convergence and numerical analysis: an application to the minimal partitions problem. Ricerche Mat., XL (1991), 33–64. CV

[3] G. Bellettini: A numerical approach to a minimum problem with applications in image segmentations. Ann. Univ. Ferrara, XXXVI (1990), 99–111. CV, NA

[4] G. Bellettini, M. Paolini, C. Verdi: ??-convergence of discrete approximations to interfaces with prescribed mean curvature Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 1 (1990), 317–328. CV, NA

[5] G. Bellettini, M. Paolini, C. Verdi: Numerical minimization of geometrical type problems related to calculus of variations. Calcolo, 27 (1990), 251–278. NA, CV

[6] G. Bellettini, M. Paolini, C. Verdi: Front-tracking and variational methods to approximate interfaces with prescribed mean curvature. Proc. Numerical Methods for Free Boundary Problems (Jyv¨askyl¨a, 1990, P. Neittaanm¨aki ed.), Birkh¨auser, Basel (1991), 83–92. NA, CV

[7] G. Bellettini, M. Paolini, C. Verdi: Convergence of discrete approximations to sets of prescribed mean curvature. Free boundary problems involving solids, Pitman Research Notes in Mathematics

Series (J.M. Chadam and H. Rasmussen, eds.) Longman Scientific & Technical Harlow, 281 (1993), 164–169. CV, NA

[8] G. Bellettini, M. Paolini, C. Verdi: Convex approximations of functionals with curvature. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 2 (1991), 297–306. CV

[9] G. Bellettini, M. Paolini, C. Verdi: Numerical minimization of functionals with curvature by convex approximations. Progress in partial differential equations: calculus of variations, applications , Pitman Research Notes in Mathematics Series (C. Bandle, J. Bemelmans, M. Chipot, M. Gr¨uter and J. Saint Jean Paulin, eds.) Longman Scientific & Technical Harlow 267 (1992), 124–138. CV, NA

[10] G. Bellettini, G. Dal Maso, M. Paolini: Semicontinuity and relaxation properties of a curvature depending functional in 2D. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 20 (1993), 247–297. CV

[11] M. Amar, G. Bellettini: A notion of total variation depending on a metric with discontinuous coefficients Ann. Inst. H. Poincar´e Anal. Non Lin´eaire, 11 (1994), 91–133. CV

[12] G. Bellettini, A. Coscia: Approximation of a functional depending on jumps and corners. Boll. Un. Mat. Ital. (7) B, (7) (1994), 151–181. CV

[13] G. Bellettini, M. Paolini: Quasi-optimal error estimates for the mean curvature flow with a forcing term. Differential Integral Equations, 8 (1995), 735–752. GEP

[14] M. Amar, G. Bellettini: Approximation by ??-convergence of a total variation with discontinuous coefficients. Asymptotic Anal., 10 (1995), 225–243. CV

[15] G. Bellettini, M. Paolini: Variational properties of an image segmentation functional depending on contours curvature. Adv. Math. Sci. Appl., 5 (1995), 681–715. CV

[16] M. Amar, G. Bellettini: A total variation with discontinuous coefficients: variational properties and approximation by ??-convergence. Atti Sem. Mat. Fis. Univ. Modena, XLIII (1995), 431–435 CV

[17] G. Bellettini, A. Coscia: Discrete approximation of a free discontinuity problem. Num. Funct. An. Opt , 3,4 (1994), 202–224. CV, NA

[18] G. Bellettini, M. Paolini: Convex approximations of an inhomogeneous anisotropic functional. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 5 (1994), 177–188. CV

[19] G. Bellettini, M. Paolini: Two examples of fattening for the curvature flow with a driving force.

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 5 (1994), 229–236. GEP

[20] G. Bellettini, M. Paolini: Numerical simulations of measurements of capillary contact angles. IMA J. Numer. Anal., 16 (1996), 165–178. NA

[21] M. Amar, G. Bellettini, S. Venturini: Integral representation of functionals defined on curves of W1,p, Proc. Roy. Soc. Edinburgh Sect. A, 128 (1998), 193–217. CV

[22] G. Bellettini, M. Paolini: Teoremi di confronto tra diverse nozioni di movimento secondo la curvatura media. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. (9) Mat. Appl., 6 (1995), 45–54. GEP

[23] G. Bellettini, M. Paolini, S. Venturini: Some results on surface measures in Calculus of Variations. Ann. Mat. Pura Appl., CLXX (1996), 329–359. CV

[24] G. Bellettini, M. Paolini: Anisotropic motion by mean curvature in the context of Finsler geometry. Hokkaido Math. J., 25 (1996), 537–566. GEP

[25] G. Alberti, G. Bellettini, M. Cassandro, E. Presutti: Surface tension in Ising systems with Kac potentials. J. Stat. Phys., 82 (1996), 743–796. SM, CV

[26] G. Bellettini, M. Paolini: Some results on minimal barriers in the sense of De Giorgi applied to driven motion by mean curvature. Rend. Acc. Naz. Sci. XL Mem. Mat., XIX (1995), 43–67 GEP

[27] G. Bellettini, M. Cassandro, E. Presutti: Constrained minima for non local functionals. J. Stat. Phys., 84 (1996), 1337–1349. CV, SM

[28] G. Bellettini: Variational approximation of functionals with curvatures and related properties. J. Convex Anal., 4 (1997), 91–108. CV

[29] G. Bellettini: Alcuni risultati sulle minime barriere per movimenti geometrici di insiemi. Boll. Un. Mat. Ital. (7), (1997), 485–512. GEP

[30] G. Bellettini, G. Fusco: The dynamic of V = H − H: motion of a small drop on a fixed surface. Proc. of the Conference on Differential Equations, Lisboa, (Eds: L. Magalhaes, C. Rocha, S. Sanchez) World Scientific, Singapore (1995), 26–38. GEP

[31] G. Bellettini, P. Colli Franzone, M. Paolini: Convergence of front propagation for anisotropic bistable reaction-diffusion equations. Asympt. Anal., 15 (1997), 325–358. GEP

[32] G. Bellettini, G. Fusco: Some aspects of the dynamic of V = H − H. J. Differential Equations, 157 (1999), 106–146. CV, GEP

[33] G. Bellettini, A. Coscia, G. Dal Maso: Compactness and lower semicontinuity properties in SBD(Omega), Math. Z., 228 (1998), 337–351. CV

[34] G. Alberti, G. Bellettini: A non local anisotropic model for phase transitions. Part 1: the optimal profile problem. Math. Ann., 310 (1998), 527–560. CV

[35] G. Bellettini, M. Novaga: Comparison results between minimal barriers and viscosity solutions for geometric evolutions. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), XXVI (1998), 97–131. GEP

[36] G. Bellettini, M. Novaga: Barriers for a class of geometric evolution problems. Atti Acc. Naz. Lincei Cl. Sc. Mat. Fis. Natur. (9) Mat. Appl., 8 (1997), 119–128. GEP

[37] G. Bellettini, M. Novaga: Minimal barriers for geometric evolutions. J. Differential Equations, 139 (1997), 76–103. GEP

[38] G. Bellettini, M. Novaga: Some aspects of De Giorgi’s barriers for geometric evolutions. Calculus of Variations and Partial Differential Equations, Springer-Verlag (1999), 115–151. GEP

[39] G. Alberti, G. Bellettini: A nonlocal anisotropic model for phase transitions, part II. Asymptotic behaviour of rescaled energies. European J. Appl. Math., 9 (1998), 285–304. CV

[40] G. Bellettini, M. Novaga: A result on motion by mean curvature in arbitrary codimension. Diff. Geom. Appl., 11 (1999), 205–220.

[41] G. Bellettini, M. Novaga, M. Paolini: An example of three-dimensional fattening for linked space curves evolving by curvature. Comm. Partial Differential Equations, 23 (1998), 1475–1492.GEP

[42] L. Ambrosio, G. Bellettini: Movimento secondo la curvatura media. Enciclopedia Treccani , Geometria, 751-753. M

[43] G. Bellettini, R. Goglione M. Novaga: Approximation to driven motion by crystalline curvature in two dimensions. Adv. Math. Sci. Appl., 10 (2000), 467–493. GEP

[44] G. Bellettini, M. Novaga: Approximation and comparison for non-smooth anisotropic motion by mean curvature in RN. Math. Mod. Meth. Appl. Sc., 10 (2000), 1–10. GEP

[45] G. Bellettini, M. Novaga, M. Paolini: Facet-breaking for three-dimensional crystals evolving by mean curvature. Interfaces Free Bound., 1 (1999), 39–55. GEP

[46] G. Bellettini, I. Fragal`a: Elliptic approximations to prescribed mean curvature surfaces in Finsler geometry. Asymp. Anal., 22 (2000), 87–111. CV

[47] G. Bellettini, G. Bouchitt´e , I. Fragal`a: BV functions with respect to a measure and relaxation of metric integral functionals. J. Convex Anal., 6 (1999), 349–366. CV

[48] G. Bellettini, G. Fusco: Stable dynamics of spikes in solutions to a system of activator-inhibitor type. Proc. of the workshop ”New trends in nonlinar partial differential equations”, (Y. Morita,

H. Ninomiya, E. Yanagida and S. Yotsutani eds.) Ryukoku Extension Center, June 7–10 (1999), 1–11. GEP

[49] G. Bellettini, M. Novaga, M. Paolini: On a crystalline variational problem, part I: first variation and global L∞-regularity. Arch. Ration. Mech. Anal., 157 (2001) 3, 165–191. CV, GEP

[50] G. Bellettini, M. Novaga, M. Paolini: On a crystalline variational problem, part II: BV -regularity and structure of minimizers on facets. Arch. Ration. Mech. Anal., 157 (2001) 3, 193–217. (1999). CV, GEP

[51] G. Bellettini, P. Butt`a, E. Presutti: Sharp interface limits of non local anisotropic interactions. Arch. Ration. Mech. Anal., 159 (2001), 109–135. GEP, SM

[52] G. Bellettini: Some aspect of motion by mean curvature in presence of nonsmooth anisotropies. Proc. of the 3th European Conference on Math., Barcellona 2000, Birkh¨auser (2001), 245-253. GEP

[53] G. Bellettini, G. Fusco: Stable dynamics of spikes in solutions to a system of reaction-diffusion equations. Asymp. Anal., 26 (2001), 307–357. CV

[54] G. Bellettini, M. Novaga, M. Paolini: Characterization of ‘facet–breaking for nonsmooth mean curvature flow in the convex case. Interfaces Free Bound., 3, (2001), 415–446. CV, GEP

[55] G. Bellettini, V. Caselles, M. Novaga: The total variation flow in Rn. J. Differential Equations, 184 (2002), 475–525. GEP

[56] G. Bellettini, R. March: Variational properties of a model for image segmentation with overlapping regions, Progress in Nonlinear Differential Equations and Their Applications, 51, 9–17 (2002), Birkh¨auser, Boston. CV

[57] G. Bellettini, M. Paolini: Errata corrige to the paper: Some results on minimal barriers in the sense of De Giorgi applied to driven motion by mean curvature. Rend. Acc. Naz. Sci. XL Mem. Mat., XXVI (2002), 161–165. GEP

[58] G. Bellettini, G. Fusco: Stable dynamics of spikes in solutions to a system of reaction-diffusion equations, II. Asymp. Anal., 33 (2003), 9–50. CV

[59] G. Bellettini, G. Fusco, G.F. Gronchi: Regularization of the two-body problem via smoothing the potential, Commun. Pure Appl. Anal., 2 (2003), 323–353. M

[60] G. Bellettini, A. Braides, G. Riey: Variational approximation of anisotropic functionals on partitions, Ann. Mat. Pura Appl., 184 (2005), 75–93. CV

[61] G. Bellettini, R. March: An image segmentation variational model with free discontinuities and contour curvature, Math. Mod. Meth. Appl. Sci., 14 (2004), 1–45. CV

[62] G. Bellettini: Nuova voce sul Dizionario Bompiani delle Opere e dei Personaggi: il teorema di De Giorgi. M

[63] G. Bellettini, M. Novaga, G. Riey: First variation of anisotropic energies and crystalline mean curvature for partitions, Interfaces Free Bound., 5 (2003), 331–356. CV

[64] G. Bellettini, G.F. Gronchi: Barriers for systems of ODEs: an application to the two-body problem, Rend. Atti Acc. Naz. Sci. XL Mem. Mat., XXVI (2002), 145–160. M

[65] G. Bellettini, L. Mugnai: Characterization and representation of the lower semicontinuous envelope of the elastica functional, Ann. Inst. H. Poincar´e Anal. Non Lin´eaire, 21 (2004), 839–880. CV

[66] G. Bellettini, V. Caselles, M. Novaga: Explicit solutions of the eigenvalue problem −div(Du/|Du|) = u, SIAM J. Math. Anal., 36 (2005), 1095–1129. GEP

[67] G. Bellettini: Barriers, fattening and mean curvature flow, Int. J. Math. Game Theory and Algebra, 14 (2004), 57–71. GEP

[68] G. Bellettini, G. Fusco: A regularized Perona-Malik functional: some aspects of the gradient dynamics, EQUADIFF 2003 Proceedings of the International Conference on Differential Equations, Hasselt, Belgium 22 - 26 July 2003 (Freddy Dumortier, Henk Broer, Jean Mawhin, Andre Vanderbauwhede and Sjoerd Verduyn Lunel eds.), 639–644. World Scientific, 2005. BFPE

[69] G. Bellettini: Anisotropic and crystalline mean curvature flow, A Sampler of Riemann-Finsler Geometry (D. Bao, R. L. Bryant, S.-S. Chern, Z. Shen eds.), Mathematical Sciences Research Institute Publications, 50 2004, Cambridge Univ. Press, 49–83. GEP

[70] G. Bellettini: On facets-breaking for crystalline mean curvature in 3D, Periodica Mathematica Hungarica, 48 (2004), 185–206. GEP

[71] G. Bellettini: An introduction to mean curvature flow, in ”Topics in Mathematical Analysis”, ISAAC Series on Analysis, Applications and Computation, vol. 3, (P. Ciatti, E. Gonzalez, M. Lanza de Cristoforis, G.P. Leonardi eds.), 63–102, World Scientific Publishing, 2008. GEP

[72] G. Bellettini, L. Mugnai: On the approximation of the elastica functional in radial symmetry, Calc. Var. Partial Differential Equations, 24, 1–20 (2005). CV

[73] G. Bellettini, A. De Masi, E. Presutti: Tunnelling for non local evolution equations, J. Nonlinear Math. Phys., 12 (2005), 50–63. SM

[74] G. Bellettini, A. De Masi, E. Presutti: Energy levels of a non local evolution equations, J. Math. Phys., 46 083302, 1–31 (2005) SM, CV

[75] G. Bellettini, V. Caselles, A. Chambolle, M. Novaga: Crystalline mean curvature flow of convex sets, Arch. Ration. Mech. Anal., 179 (2006), 109–152. GEP

[76] G. Bellettini, G. Fusco: The Gamma-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type, Trans. Amer. Math. Soc., 360 (2008), 4929–4987. CV, BFPE

[77] G. Bellettini: On gradient flows of some non-convex functionals of Perona-Malik type, Oberwol- fach Report 26/2004. BFPE

[78] G. Bellettini, M. Novaga, E. Paolini: Global solutions to the gradient flow equation of a nonconvex functional, SIAM J. Math. Anal., 37 (2006), 1657–1687. BFPE

[79] G. Bellettini, R. March: Variational problems in image segmentation and ??-convergence methods, in Advance in Image and Video Segmentation (Y.-J. Zhang ed.), IRM Press (2006), 46–71. M

[80] G. Bellettini, L. Mugnai: A varifolds representation result of the relaxed elastica functional, J. Convex Anal., 14 (2007), 543–564. CV

[81] G. Bellettini, M.S. Gelli, S. Luckhaus, M. Novaga: Deterministic equivalent for the Allen-Cahn energy of a scaling law in the Ising model, Calc. Var. Partial Differential Equations, 26 (2006), 429–445. CV

[82] G. Bellettini, M. Masala, M. Novaga: On a conjecture of De Giorgi on the squared distance function, J. Convex Anal. 14 (2007), 353–359. M

[83] G. Bellettini, R. March: Asymptotic properties of the Nitzberg-Mumford variational model for segmentation with depth, International Series of Numerical Mathematics, 154 (2007), 75–84, Birkh¨auser Verlag, Basel. CV

[84] G. Bellettini, A. De Masi, N. Dirr, E. Presutti: Tunnelling in two dimensions, Comm. Math. Phys. 269 (2007), 715-763. SM

[85] G. Bellettini, G. Fusco, N. Guglielmi: A concept of solution for forward-backward equations of the form u_t = 1/2 phi′(u_x)_x and numerical experiments for the singular perturbation u_t =−eps^2 u_xxxx + 1/2 (phi′(u_x))_x, Discrete Contin. Dyn. Syst. 16 (2006), 783-842. BFPE

[86] G. Bellettini, C. Mantegazza, M. Novaga: Singular perturbations of mean curvature flow, J. Differential Geom. 57 (2007), 403–431. GEP, M

[87] G. Bellettini, M. Chermisi, M. Novaga: The level set method for systems of PDEs, Comm. Partial Differential Equations, 32 (2007), 1043–1064. CV

[88] G. Bellettini, G. Fusco, N. Guglielmi: A possible approach to the dynamic of forward-backward parabolic equations, Proc. of the Ryukoku Workshop on Mathematical Aspects of Pattern Formation and Dynamics in Dissipative Systems, 2004. BFPE

[89] G. Bellettini, B. Dacorogna, G. Fusco, F. Leonetti: Qualitative properties of Lipschitz solutions of eikonal type systems, Adv. Math. Sci. Appl., 16 (2006), 259–274. CV

[90] G. Bellettini, M. Chermisi, M. Novaga: Crystalline curvature flow of networks, Interfaces Free Bound., 8 (2006), 481–521. GEP

[91] G. Bellettini, A. De Masi, N. Dirr, E. Presutti: Stability of invariant manifolds in one and two dimensions, Nonlinearity, 20 (2007), 537–582. SM

[92] G. Bellettini, L. Mugnai: Some aspect of the variational nature of mean curvature flow, J. Eur. Math. Soc., 10 (2008), 1013-1036. GEP

[93] G. Bellettini, V. Beorchia, M. Paolini: Topological and variational properties of a model for the reconstruction of three-dimensional transparent images with self-occlusions, J. Math. Imaging Vision, 32 (2008), 265–291. CV, M

[94] G. Bellettini: On singular perturbations of some partial differential equations, Oberwolfach Report, Mini-Workshop: Anisotropic Motion Law, 38/2006, 2283-2284. CV

[95] LARES collaboration: Int. J. Modern Physics D, 16 12A (2007) 2271-2285, World Scientific Publishing Company. M

[96] LARES collaboration: Probing gravity in the Earth-Moon system with ETRUSCO,Moon-LIGHT and LAGEOS, in Frontier Objects in Astrophysics and Particle Physics, Vulcano Workshop 2008,F. Giovannelli and G. Mannocchi Eds., Societ`a Italiana di Fisica, Bologna, Atti di Conferenze, vol. 98, Vulcano 26-31 maggio 2008, 533-544. M

[97] G. Bellettini, M. Novaga, M. Paolini, C. Tornese: Convergence of discrete schemes for the Perona- Malik equation, J. Differential Equations, 245 (2008), 892–924. BFPE

[98] G. Bellettini: Topological and variational properties of a model for reconstructing threedimensional images, Oberwolfach Reports, Trends in Mathematical Imaging and Surface Processing, 3/2007, 147-148. CV, M

[99] G. Bellettini: ??-convergence and one-dimensional scalar hyperbolic conservation laws, Oberwolfach Reports, Phase Transitions 28/2007, 1579-1580. HPDE

[100] G. Bellettini, V. Caselles, A. Chambolle, M. Novaga: The volume preserving crystalline meancurvature flow of convex sets in RN, J. Math. Pures Appliqu´ee, 92(5) (2009), 499-527. GEP

[101] G. Bellettini, V. Beorchia, M. Paolini: An explicit formula for a Bennequin-type invariant for apparent contours, Topology Appl. 156 (2009), 747–760. M

[102] LARES collaboration: The design of LARES: a satellite for testing general relativity. 58th International Astronautical Congress, Hyderabad, India, 24-28 September 2007, IAF/IAA. M

[103] G. Bellettini, M. Novaga, M. Paolini, C. Tornese: Classification of the equilibria and Gamma-convergence for the semi-discrete Perona-Malik functional, Calcolo 46(4) (2009), 221–243. BFPE

[104] G. Bellettini, L. Bertini, M. Mariani, M. Novaga: Gamma-entropy cost for conservation laws, Arch. Ration. Mech. Anal. 195 (2010), 261-309. HPDE

[105] G. Bellettini, L. Mugnai: Anisotropic geometric functionals and gradient flows, Banach Cent. Publ., vol. 86 (2009), 21–43. CV

[106] MOONLIGHT collaboration: MoonLIGHT-R: Moon Laser Instrumentation for General Relativity High-accuracy Tests, Proc. XLII Rencontres de Moriond, La Thuile, in Gravitational Waves and Experimental Gravity, (J. Dumarchez and J.Tran Thanh Van eds.), 2007. M

[107] G. Bellettini, M. Novaga, M. Paolini: Convergence for long-times of a semidiscrete Perona-Malik equation in one dimension, Math. Models Meth. Appl. Sci. 21 (2) (2011), 1–25. BFPE

[108] G. Bellettini: On facet breaking for crystalline mean curvature flow in 3D, On the convergence of discrete schemes for the Perona-Malik equation, On some topological and variational properties of a model for reconstructing transparent images with self-occlusions. Proc. International Conference in Mathematics, Z¨urich 2007. PAMM Proc. Appl. Math. Mech. 7, 1041901-1041902 (2007)/DOE 10.1002/ pamm.200700044, PAMM Proc. Appl. Math. Mech. 7, 1023401-1023402 (2007)/DOE 10.1002/ pamm.200700438, PAMM Proc. Appl. Math. Mech. 7, 1041909-1041910 (2007)/DOE 10.1002/ pamm.200700552, M

[109] G. Bellettini, V. Beorchia, M. Paolini: Completion of visible contours, SIAM J. Imaging Sci. 2 (2009), 777-799. M

[110] G. Bellettini, F. Caselli,M.Mariani: Some applications of the least squaresmethod to differential equations, Singularities in Nonlinear Evolution Phenomena and Applications, Proceedings, M. Novaga, G. Orlandi Eds. Pubbl. Cent. Ric. Mat. Ennio De Giorgi, 59–87, 2009. HPDE

[111] G. Bellettini, M. Novaga, G. Orlandi: Time-like lorentzian minimal submanifolds as singular limits of nonlinear wave equations, Physica D 239 (2010), 335-339. HPDE

[112] G. Bellettini, V. Beorchia, M. Paolini: Completeness of Reidemeister-type moves for surfaces embedded in three-dimensional space, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 22 (2011), 1–19. M

[113] G. Bellettini, F. Caselli, M. Mariani: Quasi-potentials of the entropy functionals for scalar conservation laws, J. Funct. Anal. 258-2 (2010), 534-558. HPDE

[114] G. Bellettini, M. Novaga: Curvature evolution of nonconvex lens-shaped domains, J. Reine Angew. Math. 656 (2011), 17–46. GEP

[115] G. Bellettini, L. Mugnai: Approximation of the Helfrich’s functional via diffuse Interfaces, SIAM J. Math. Anal. 42 (2010), 2402-2433. CV

[116] G. Bellettini, M. Paolini: On the area of the graph of a singular map from the plane to the plane taking three values, Adv. Calc. Var. 3 (2010), 371–386. CV

[117] G. Bellettini, J. Hoppe, M. Novaga, G. Orlandi: Closure and convexity properties of closed relativistic strings, Complex Anal. Oper. Theory 4 (2010), 473–496. HPDE

[118] G. Bellettini: Minimal timelike lorentzian submanifolds as limits of singularly perturbed wave equations, Oberwolfach Report, 2010, in ”New Directions in Simulations, Control and Analysis for Interfaces and Free Boundaries”, 265-266. BFPE

[119] MAGIA collaboration: Fundamental physics and absolute positioning metrology with the MAGIA lunar orbiter, Experimental Astronomy 17, (2010), 1–17. M

[120] G. Bellettini, M. Mariani: Variational convergence of multidimensional conservation laws, Bull. Greek Math. Soc. 57 (2010), 31–45. HPDE

[121] R. March, G. Bellettini, R. Tauraso, S. Dell’Agnello: Constraining spacetime torsion with the Moon and Mercury, Phys. Rev. D 83, 104008-18, 2011. M

[122] R. March, G. Bellettini, R. Tauraso, S. Dell’Agnello: Constraining spacetime torsion with LAGEOS, Gen. Rel. Gravitation 43 (2011), 3099-3126. M

[123] G. Bellettini: An introduction to anisotropic and crystalline mean curvature flow, Sapporo University, Internal reports, August 2010. GEP

[124] G. Bellettini: Reconstruction of a 3D shape from its apparent contour, Oberwolfach Report 07/2011, Trends in Mathematical Imaging and Surface Processing, 12–15. M

[125] G. Bellettini, M. Novaga, G. Orlandi: Lorentzian varifolds and applications to closed relativistic string, Indiana Univ. Math. J., to appear. GEP

[126] G. Bellettini: Remarks on the limit of the Cahn-Hilliard equation in 1D, type, Oberwolfach Report 2011. BFPE

[127] G. Bellettini, L. Bertini, M. Mariani, M. Novaga: Convergence of the one-dimensional Cahn- Hilliard equation, SIAM J. Math. Anal. 44 (2012), 3458–3480. BFPE

[128] G. Bellettini, M. Paolini, F. Pasquarelli: Nonconvex mean curvature flow as a formal singular limit of the nonlinear bidomain model, submitted. BFPE

[129] G. Bellettini, C. Geldhauser, M. Novaga, Convergence of a semidiscrete scheme for a forwardbackward parabolic equation, Adv. Differential Equations, 18 (2013), 495-522. BFPE

[130] R. March, G. Bellettini, R. Tauraso, S. Dell’Agnello, Constraining spacetime torsion with the Moon, Mercury and LAGEOS, Acta Polytechnica, to appear. M

[131] G. Bellettini, A. Chambolle, M. Goldman: The Gamma-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension, submitted. CV

[132] S. Amato, G. Bellettini, M. Paolini: The nonlinear multidomain model: a new formal asymptotic analysis, Singularities in Nonlinear Evolution Phenomena and Applications, Proceedings,

M. Novaga, G. Orlandi Eds. Pubbl. Cent. Ric. Mat. Ennio De Giorgi, to appear. BFPE

[133] G. Bellettini: On the area of the graph of a map from the plane to the plane with a line discontinuity, Oberwolfach Report 2013, to appear. BFPE

8. Books

G. Bellettini: Lectures on Mean Curvature flow: Minimal Barriers and Singular Perturbations, Edizioni della Scuola Normale Superiore di Pisa/Birkha¨user, to appear.

G. Bellettini, V. Beorchia, M. Paolini, F. Pasquarelli: 3D Shapes Reconstruction from Apparent Contours. Theory and Algorithmic Applications, Computational Imaging and Vision, Springer-Verlag, in preparation