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Finite Difference Approximation of Free Discontinuity Problems

Massimo Gobbino·Maria Giovanna Mora
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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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BibTeXRIS

Massimo Gobbino, Maria Giovanna Mora. 2000-06-08. Finite Difference Approximation of Free Discontinuity Problems. https://arxiv.org/abs/math/0006059

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