Finite-difference approximation of free-discontinuity problems

Author： Gobbino Massimo   Mora Maria Giovanna  

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.131, Iss.3, 2001-06, pp. : 567-595

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Abstract

We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence and a compactness result, which implies, in particular, the convergence of minima and minimizers.

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