Free Access
Volume 46, Number 2, November-December 2012
Page(s) 389 - 410
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]
  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]
  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]
  4. L. Ambrosio and V.M. Tortorelli, On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. B 6 (1992) 105–123. [MathSciNet]
  5. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford (2000).
  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]
  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]
  8. A. Blake and A. Zisserman, Visual Reconstruction. MIT Press, Cambridge, MA (1987).
  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]
  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]
  11. A. Braides, Lower semicontinuity conditions for functionals on jumps and creases. SIAM J. Math Anal. 26 (1995) 1184–1198. [CrossRef] [MathSciNet]
  12. A. Braides, Approximation of Free-discontinuity Problems. Springer Verlag, Berlin (1998).
  13. A. Braides, Γ-convergence for Beginners. Oxford University Press, Oxford (2002).
  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.
  15. A. Braides and M.S. Gelli, Limits of discrete systems with long-range interactions. J. Convex Anal. 9 (2002) 363–399.
  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]
  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]
  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]
  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.
  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]
  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
  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]
  23. M. Carriero, A. Leaci and F. Tomarelli, A Dirichlet problem with free gradient discontinuity. Adv. Mat. Sci. Appl. 20 (2010) 107–141
  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]
  25. A. Chambolle, Un théorème de Γ-convergence pour la segmentation des signaux. C. R. Acad. Sci., Paris, Ser. I 314 (1992) 191–196.
  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]
  27. A. Chambolle, Finite-differences approximation of the Mumford-Shah functional. ESAIM: M2AN 33 (1999) 261–288. [CrossRef] [EDP Sciences]
  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]
  29. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Co., Amsterdam (1978).
  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]
  31. S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE PAMI 6 (1984) 721–724. [CrossRef] [PubMed]
  32. W.E.L. Grimson, From Images to Surfaces. The MIT Press Classic Series. MIT, Cambridge (1981).
  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]
  34. P. Santos and E. Zappale, Lower Semicontinuity in SBH. Mediterranean J. Math. 5 (2008) 221–235. [CrossRef]
  35. B. Schmidt, On the derivation of linear elasticity from atomistic models. Netw. Heterogen. Media 4 (2009) 789–812. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you