# Partial regularity for degenerate variational problems and image restoration models in $\rm BV$

created by schmidt on 30 May 2012
modified on 11 Jun 2014

[BibTeX]

Published Paper

Inserted: 30 may 2012
Last Updated: 11 jun 2014

Journal: Indiana Univ. Math. J.
Volume: 63
Number: 1
Pages: 213-279
Year: 2014
We establish partial and local ${\rm C}^{1,\alpha}$-regularity results for vectorial almost-minimizers of convex variational integrals in $\rm BV$. In particular, we investigate cases with a degenerate or singular behavior of $p$-Laplace type, and we cover (local) minimizers of the exemplary integrals $\int_\Omega(1+\lvert\nabla w\rvert^p)^\frac1p\,{\rm d}x$ with $1< p<\infty$. We also treat some related models with lower-order terms, which are motivated by image restoration.