Jule Helena Schütt | Searcharxiv

arXiv2026

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

We revisit the partial $\mathrm{C}^{1,α}$ regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the Hölder exponent $α$ on structural assumptions for general zero-order terms. A particular case of our conclusions carries over to the parametric setting of Massari's regularity theorem for prescribed-mean-curvature hypersurfaces and there confirms optimal regularity up to the limit exponent.

math.AP↗

arXiv2025

The Optimal Hölder Exponent in Massari's Regularity Theorem

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.

math.AP↗