Accepted Paper

Inserted: 6 oct 2024
Last Updated: 11 mar 2025

Journal: J. Lond. Math. Soc., II. Ser.
Year: 2025

Abstract:

We revisit the partial $\mathrm{C}^{1,\alpha}$ regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the Hölder exponent $\alpha$ 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.

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