Open Access
Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 70 | |
Number of page(s) | 14 | |
DOI | https://doi.org/10.1051/cocv/2024060 | |
Published online | 07 October 2024 |
- 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]
- G. David, Singular sets of minimizers for the Mumford-Shah functional. Vol. 233 of Progress in Mathematics. Birkhauser Verlag, Basel (2005). [Google Scholar]
- G.A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (1998) 1319–1342. [Google Scholar]
- E. De Giorgi, M. Carriero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal. 108 (1989) 195–218. [CrossRef] [MathSciNet] [Google Scholar]
- L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000). [CrossRef] [Google Scholar]
- L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via r-convergence. Commun. Pure Appl. Math. 43 (1990) 999–1036. [CrossRef] [Google Scholar]
- 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]
- X. Feng and A. Prohl, Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting. M2AN Math. Model. Numer. Anal. 38 (2004) 291–320. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- J.W. Barrett, X. Feng and A. Prohl, Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation. M2AN Math. Model. Numer. Anal. 40 (2006) 175–199. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- M. Struwe, Geometric evolution problems, in Nonlinear partial differential equations in differential geometry. Vol. 2 of IAS/Park City Math. Ser. American Mathematical Society, Providence, RI (1996) 257–339. [Google Scholar]
- L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 13 (1959) 115–162. [MathSciNet] [Google Scholar]
- W.R. Wade, The bounded convergence theorem. Am. Math. Monthly 81 (1974) 387–389. [CrossRef] [Google Scholar]
- J.-P. Aubin, Un theoreme de compacite. C. R. Acad. Sci. Paris 256 (1963) 5042–5044. [MathSciNet] [Google Scholar]
- J.-L. Lions, Quelques methodes de resolution des problèmes aux limites non linéaires. Dunod, Paris; Gauthier-Villars, Paris (1969). [Google Scholar]
- J. Simon, Compact sets in the space Lp(0,T; B). Ann. Mat. Pura Appl. 146 (1987) 65–96. [Google Scholar]
- L.C. Evans, Partial differential equations. Vol. 19 of Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence, RI (2010). [Google Scholar]
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.