Free Access
Issue
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
Page(s) 389 - 410
DOI https://doi.org/10.1051/m2an/2011043
Published online 23 November 2011
  1. R. Alicandro and M. Cicalese, A general integral representation result for continuum limits of discrete energies with superlinear growth. SIAM J. Math. Anal. 36 (2004) 1–37. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Alicandro, M. Focardi and M.S. Gelli, Finite difference approximation of energies in fracture mechanics. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 29 (2000) 671–709. [MathSciNet] [Google Scholar]
  3. L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence. Comm. Pure Appl. Math. 43 (1990) 999–1036. [CrossRef] [MathSciNet] [Google Scholar]
  4. L. Ambrosio and V.M. Tortorelli, On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. B 6 (1992) 105–123. [MathSciNet] [Google Scholar]
  5. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000). [Google Scholar]
  6. L. Ambrosio, L. Faina and R. March, Variational approximation of a second order free discontinuity problem in computer vision. SIAM J. Math. Anal. 32 (2001) 1171–1197. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Bellettini and A. Coscia, Approximation of a functional depending on jumps and corners. Boll. Un. Mat. Ital. B 8 (1994) 151–181. [MathSciNet] [Google Scholar]
  8. A. Blake and A. Zisserman, Visual Reconstruction. MIT Press, Cambridge, MA (1987). [Google Scholar]
  9. B. Bourdin and A. Chambolle, Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. Numer. Math. 85 (2000) 609–646. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Brady and B.K.P. Horn, Rotationally symmetric operators for surface interpolation. Computer Vision, Graphics, and Image Processing 22 (1983) 70–94. [CrossRef] [Google Scholar]
  11. A. Braides, Lower semicontinuity conditions for functionals on jumps and creases. SIAM J. Math Anal. 26 (1995) 1184–1198. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Braides, Approximation of Free-discontinuity Problems. Springer Verlag, Berlin (1998). [Google Scholar]
  13. A. Braides, Γ-convergence for Beginners. Oxford University Press, Oxford (2002). [Google Scholar]
  14. A. Braides, Discrete approximation of functionals with jumps and creases, in Homogenization, 2001 (Naples) GAKUTO Internat. Ser. Math. Sci. Appl. 18. Tokyo, Gakkōtosho (2003) 147–153. [Google Scholar]
  15. A. Braides and M.S. Gelli, Limits of discrete systems with long-range interactions. J. Convex Anal. 9 (2002) 363–399. [Google Scholar]
  16. A. Braides and A. Piatnitski, Overall properties of a discrete membrane with randomly distributed defects. Arch. Ration. Mech. Anal. 189 (2008) 301–323. [CrossRef] [MathSciNet] [Google Scholar]
  17. A. Braides, A.J. Lew and M. Ortiz, Effective cohesive behavior of layers of interatomic planes. Arch. Ration. Mech. Anal. 180 (2006) 151–182. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Braides, M. Solci and E. Vitali, A derivation of linear elastic energies from pair-interaction atomistic systems. Netw. Heterog. Media 2 (2007) 551–567 [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Carriero, A. Leaci and F. Tomarelli, A second order model in image segmentation: Blake and Zisserman functional, in Variational Methods for Discontinuous Structures (Como, 1994), Progr. Nonlin. Diff. Eq. Appl. 25, edited by R. Serapioni and F. Tomarelli. Basel, Birkhäuser (1996) 57–72. [Google Scholar]
  20. M. Carriero, A. Leaci and F. Tomarelli, Strong minimizers of Blake and Zisserman functional. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 (1997) 257–285. [MathSciNet] [Google Scholar]
  21. M. Carriero, A. Leaci and F. Tomarelli, Density estimates and further properties of Blake and Zisserman functional, in From Convexity to Nonconvexity, Nonconvex Optim. Appl. 55, edited by R. Gilbert and Pardalos. Kluwer Acad. Publ., Dordrecht (2001) 381–392 [Google Scholar]
  22. M. Carriero, A. Leaci and F. Tomarelli, Euler equations for Blake and Zisserman functional. Calc. Var. Partial Diff. Eq. 32 (2008) 81–110. [CrossRef] [Google Scholar]
  23. M. Carriero, A. Leaci and F. Tomarelli, A Dirichlet problem with free gradient discontinuity. Adv. Mat. Sci. Appl. 20 (2010) 107–141 [Google Scholar]
  24. M. Carriero, A. Leaci and F. Tomarelli, A candidate local minimizer of Blake and Zisserman functional. J. Math Pures Appl. 96 (2011) 58–87 [CrossRef] [Google Scholar]
  25. A. Chambolle, Un théorème de Γ-convergence pour la segmentation des signaux. C. R. Acad. Sci., Paris, Ser. I 314 (1992) 191–196. [Google Scholar]
  26. A. Chambolle, Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations. SIAM J. Appl. Math. 55 (1995) 827–863. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Chambolle, Finite-differences approximation of the Mumford-Shah functional. ESAIM: M2AN 33 (1999) 261–288. [CrossRef] [EDP Sciences] [Google Scholar]
  28. A. Chambolle and G. Dal Maso, Discrete approximation of the Mumford-Shah functional in dimension two. ESAIM: M2AN 33 (1999) 651–672. [CrossRef] [EDP Sciences] [Google Scholar]
  29. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Co., Amsterdam (1978). [Google Scholar]
  30. S. Conti, I. Fonseca and G. Leoni A Γ-convergence result for the two-gradient theory of phase transitions. Comm. Pure Appl. Math. 55 (2002) 857–936. [CrossRef] [MathSciNet] [Google Scholar]
  31. S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE PAMI 6 (1984) 721–724. [CrossRef] [PubMed] [Google Scholar]
  32. W.E.L. Grimson, From Images to Surfaces. The MIT Press Classic Series. MIT, Cambridge (1981). [Google Scholar]
  33. D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42 (1989) 577–685. [CrossRef] [MathSciNet] [Google Scholar]
  34. P. Santos and E. Zappale, Lower Semicontinuity in SBH. Mediterranean J. Math. 5 (2008) 221–235. [CrossRef] [Google Scholar]
  35. B. Schmidt, On the derivation of linear elasticity from atomistic models. Netw. Heterogen. Media 4 (2009) 789–812. [CrossRef] [Google Scholar]

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