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

## Schmidt Thomas

published
year: 2014
journal: Indiana Univ. Math. J.
abstract: 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.

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