Finite Difference Approximation of Free Discontinuity Problems

Details Finite Difference Approximation of Free Discontinuity Problems Finite Difference Approximation of Free Discontinuity Problems

2000-06-08

arxiv.org/abs/math/0006059v1

Mathematics

Functional Analysis

39 pages. to appear on Proc. Royal Soc. Edinb. Ser. A

Scientific paper

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, $\Gamma$-convergence, and a compactness result which
implies, in particular, the convergence of minima and minimizers.

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