An approximation result for free discontinuity functionals by means of non-local energies

DOI10.1002/mma.1019zbMath1357.49156OpenAlexW2077274411MaRDI QIDQ3541232

Luca Lussardi

Publication date: 25 November 2008

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1019

zbMATH Keywords

relaxationfree discontinuitiesvariational approximationmethods involving semicontinuity and convergencevariational problems in a geometric measure-theoretic setting

Mathematics Subject Classification ID

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

Related Items (2)

On non-locality in the calculus of variations ⋮ Eigendamage: an eigendeformation model for the variational approximation of cohesive fracture -- a one-dimensional case study

Cites Work

• Approximation of free-discontinuity problems
• Sequences of non-local functionals which approximate free-discontinuity problems
• Free-discontinuity problems via functionals involving the \(L^1\)-norm of the gradient and their approximations
• Non-local approximation of the Mumford-Shah functional
• Non-local approximation of free-discontinuity functionals with linear growth: the one dimensional case
• Finite-difference approximation of free-discontinuity problems
• Approximation of functional depending on jumps by elliptic functional via t-convergence
• Relaxation results for some free discontinuity problems.
• A density result in SBV with respect to non-isotropic energies
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