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

Negri, Matteo
January 2006
Calculus of Variations & Partial Differential Equations;Jan2006, Vol. 25 Issue 1, p33
Academic Journal
We consider a class of functionals which are defined in the spaces SBV and SBD and which do not depend on the traces u � on the set of discontinuity points. In this work we prove that it is possible to approximate these energies, in the sense of G-convergence, by means of a family of non-local functionals defined in Sobolev spaces. Moreover we illustrate some applications for image processing and mechanics.


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