A1 Journal article (refereed)
Local regularity for quasi-linear parabolic equations in non-divergence form (2020)

Attouchi, A. (2020). Local regularity for quasi-linear parabolic equations in non-divergence form. Nonlinear Analysis : Theory, Methods and Applications, 199, Article 112051. https://doi.org/10.1016/j.na.2020.112051

JYU authors or editors

Publication details

All authors or editors: Attouchi, Amal

Journal or series: Nonlinear Analysis : Theory, Methods and Applications

ISSN: 0362-546X

eISSN: 1873-5215

Publication year: 2020

Volume: 199

Article number: 112051

Publisher: Elsevier

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1016/j.na.2020.112051

Publication open access: Not open

Publication channel open access: 

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1809.03241

Abstract

We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p-Laplacian type and in non-divergence form. We provide local Hölder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Hölder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.

Keywords: partial differential equations

Free keywords: degenerate parabolic equations; regularity of the gradient; viscosity solutions

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 1