Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights

Changxing Miao; Zhiwen Zhao

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arXiv · 2210.10006

Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights

Changxing Miao·Zhiwen Zhao

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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.

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Changxing Miao, Zhiwen Zhao. 2022-10-18. Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights. https://arxiv.org/abs/2210.10006

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