IUMJ

Title: Partial regularity for degenerate variational problems and image restoration models in BV

Authors: Thomas Schmidt

Issue: Volume 63 (2014), Issue 1, 213-279

Abstract:

We establish partial and local $\mathrm{C}^{1,\alpha}$-regularity results for vectorial almost-minimizers of convex variational integrals in $BV$. In particular, we investigate cases with a degenerate or singular behavior of $p$-Laplace type, and we cover (local) minimizers of the exemplary integrals \[ \int_{\Omega}(1+|\nabla w|^p)^{1/p}\,\mathrm{d}x \] with $1<p<\infty$. We also treat some related models with lower-order terms, which are motivated by image restoration.