Gradient Regularity for Double-Phase Orthotropic Functionals

Abstract

We prove higher integrability for local minimizers of the double-phase orthotropic functional [Formula: see text] when the weight function [Formula: see text] is assumed to be [Formula: see text]-Hölder continuous, while the exponents [Formula: see text] are such that [Formula: see text] and [Formula: see text]. Under natural Sobolev regularity of [Formula: see text], we further obtain explicit Lipschitz regularity estimates for local minimizers.