On the non-local approximation of free-discontinuity problems

DOI10.1080/03605309808821367zbMath0907.49009OpenAlexW2057732970MaRDI QIDQ4212410

Andrea Braides, Adriana Garroni

Publication date: 11 January 1999

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309808821367

zbMATH Keywords

\(\Gamma\)-convergencefree discontinuity problemsspecial functions of bounded variationSBVMumford-Shah problem

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (8)

Non-local approximation of the Griffith functional ⋮ A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach ⋮ The method of moments for some one-dimensional, non-local, non-convex variational problems ⋮ Eigendamage: an eigendeformation model for the variational approximation of cohesive fracture -- a one-dimensional case study ⋮ Non-local approximation of free-discontinuity problems with linear growth ⋮ Free-discontinuity problems generated by singular perturbation ⋮ NON-LOCAL VARIATIONAL LIMITS OF DISCRETE SYSTEMS ⋮ A nonlocal approximation of free discontinuity problems in SBV and SBD

Cites Work

• Singular perturbations of variational problems arising from a two-phase transition model
• An introduction to \(\Gamma\)-convergence
• Non-local approximation of the Mumford-Shah functional
• The gradient theory of phase transitions and the minimal interface criterion
• Optimal approximations by piecewise smooth functions and associated variational problems
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• Nonconvex variational problems with anisotropic perturbations

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