Finite Difference Approximation of Free Discontinuity Problems
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
39 pages. to appear on Proc. Royal Soc. Edinb. Ser. A
39 pages. to appear on Proc. Royal Soc. Edinb. Ser. A