Calculus of Variations and Geometric Measure Theory

M. Negri

A non-local approximation of free discontinuity problems in SBV and SBD

created on 23 Jun 2004
modified by negri on 20 Dec 2006


Published Paper

Inserted: 23 jun 2004
Last Updated: 20 dec 2006

Journal: Calc. Var. Partial Differential Equations.
Volume: 25
Pages: 33-62
Year: 2006


We consider a class of functionals which are defined in the spaces $SBV$ and $SBD$ and do not depend on the traces $u^\pm$ on the set of discontinuity. In this work we prove that it is possible to approximate this energies, in the sense of $\Gamma$-convergence, by means of a family of non-local functionals, defined in Sobolev spaces. Moreover we illustrate some applications for image processing and fracture mechanics.