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

Abstract We revisit the partial regularity theory for minimizers of non‐parametric integrals with emphasis on sharp dependence of the Hölder exponent 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.