Local regularity for solutions to quasi-linear singular parabolic equations with anisotropic weights

Changxing Miao; Zhiwen Zhao

Local regularity for solutions to quasi-linear singular parabolic equations with anisotropic weights

Analysis of PDEs 2024-06-05 v4

Authors: Changxing Miao , Zhiwen Zhao

Abstract

This paper develops a concise procedure for the study on local behavior of solutions to anisotropically weighted quasi-linear singular parabolic equations of $p$ -Laplacian type, which is realized by improving the energy inequalities and applying intrinsic scaling factor to the De Giorgi truncation method. In particular, it also presents a new proof for local H\"{o}lder continuity of the solution in the unweighted case.

Keywords

local regularity quasi-linear singular parabolic equations anisotropic weights p-Laplacian De Giorgi truncation method intrinsic scaling Hölder continuity

Cite

@article{arxiv.2312.02875,
  title  = {Local regularity for solutions to quasi-linear singular parabolic equations with anisotropic weights},
  author = {Changxing Miao and Zhiwen Zhao},
  journal= {arXiv preprint arXiv:2312.02875},
  year   = {2024}
}

Comments

We achieve a concise and elegant proof by improving the energy inequalities and applying the redefined intrinsic scaling factor to the De Giorgi truncation method

Local regularity for solutions to quasi-linear singular parabolic equations with anisotropic weights

Abstract

Keywords

Cite

Comments

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