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Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights

Part of: Elliptic equations and systems Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  28 April 2023

Changxing Miao  and
Zhiwen Zhao
Changxing Miao
Affiliation:
Beijing Computational Science Research Center, Beijing 100193, China Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China (miao_changxing@iapcm.ac.cn)
Zhiwen Zhao
Affiliation:
Beijing Computational Science Research Center, Beijing 100193, China (zwzhao365@163.com)
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Abstract

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.

Keywords

local regularityanisotropic weightsweighted Poincaré inequalityweighted p-Laplace equationsweighted fast diffusion equations

MSC classification

Primary: 35B65: Smoothness and regularity of solutions 35J92: Quasilinear elliptic equations with $p$-Laplacian 35K57: Reaction-diffusion equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 2 , May 2023 , pp. 391 - 436
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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