Improved bounds for solutions of ϕ-Laplacians

Abstract

Abstract. In this short paper we prove a parametric version of the Harnack inequality for φ-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.

Hölder continuity of the minimizer of an obstacle problem with generalized Orlicz growth

“…We also refer to [15,17,27,44,48,49] for regularity results in the various variants and borderline cases. Maximal regularity for Orlicz growth was settled by Lieberman in [38] and for Hölder continuity of the solution assumptions have been relaxed in [2]. Other regularity results for Orlicz growth can be found for example in [11,12,18].…”