Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights

Abstract

The main purpose of this paper is to capture the asymptotic behavior for solutions to a class of nonlinear elliptic and parabolic equations with the anisotropic weights consisting of two power-type weights of different dimensions near the degenerate or singular point, especially covering the weighted $p$-Laplace equations and weighted fast diffusion equations. As a consequence, we also establish the local H\"{o}lder estimates for their solutions in the presence of single power-type weights.