Partial regularity for degenerate variational problems and image restoration models in BV Thomas Schmidt 49N6035J7035J7535J92variational integralspartial regularityfunctions of bounded variation 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. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5174 10.1512/iumj.2014.63.5174 en Indiana Univ. Math. J. 63 (2014) 213 - 279 state-of-the-art mathematics http://iumj.org/access/