A1 Journal article (refereed)
Gradient regularity for a singular parabolic equation in non-divergence form (2020)

Attouchi, A., & Ruosteenoja, E. (2020). Gradient regularity for a singular parabolic equation in non-divergence form. Discrete and Continuous Dynamical Systems: Series A, 40(10), 5955-5972. https://doi.org/10.3934/dcds.2020254

JYU authors or editors

Attouchi, Amal
Ruosteenoja, Eero

Publication details

All authors or editors: Attouchi, Amal; Ruosteenoja, Eero

Journal or series: Discrete and Continuous Dynamical Systems: Series A

ISSN: 1078-0947

eISSN: 1553-5231

Publication year: 2020

Volume: 40

Issue number: 10

Pages range: 5955-5972

Publisher: American Institute of Mathematical Sciences

Publication country: United States

Publication language: English

DOI: https://doi.org/10.3934/dcds.2020254

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1912.10075

Abstract

In this paper we consider viscosity solutions of a class of non-homogeneous singular parabolic equations
∂tu−|Du|γΔNpu=f,
where −1<0, 1

<∞, and f is a given bounded function. We establish interior Hölder regularity of the gradient by studying two alternatives: The first alternative uses an iteration which is based on an approximation lemma. In the second alternative we use a small perturbation argument.

Keywords: partial differential equations

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

Fields of science:

111 Mathematics (Natural sciences)

Contributing organizations

JYU units:

Department of Mathematics and Statistics

Related projects

Regularity issues for the normalized p-Laplacian and more general parabolic equations in non-divergence form.
- - Attouchi, Amal
- Academy of Finland
01/09/2017-31/08/2020

Ministry reporting: Yes

Reporting Year: 2020