Finite Difference Approximation of Free Discontinuity Problems
Functional Analysis
2007-05-23 v1
Abstract
We approximate functionals depending on the gradient of and on the behaviour of near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, -convergence, and a compactness result which implies, in particular, the convergence of minima and minimizers.
Cite
@article{arxiv.math/0006059,
title = {Finite Difference Approximation of Free Discontinuity Problems},
author = {Massimo Gobbino and Maria Giovanna Mora},
journal= {arXiv preprint arXiv:math/0006059},
year = {2007}
}
Comments
39 pages. to appear on Proc. Royal Soc. Edinb. Ser. A