The Optimal Hölder Exponent in Massari's Regularity Theorem

Abstract

We determine the optimal Hölder exponent in Massari's regularity theorem for sets with variational mean curvature in ${\mathrm{L}}^p$. In fact, we obtain regularity with improved exponents and at the same time provide sharp counterexamples.

This version (v3) corrects typos in proof of Proposition 4.1 only

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• Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem