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Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights

Published online by Cambridge University Press:  28 April 2023

Changxing Miao
Beijing Computational Science Research Center, Beijing 100193, China Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China (
Zhiwen Zhao
Beijing Computational Science Research Center, Beijing 100193, China (


The main purpose of this paper is to capture the asymptotic behaviour 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 Hölder estimates for their solutions in the presence of single power-type weights.

Research Article
© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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