A1 Journal article (refereed)
On the second-order regularity of solutions to the parabolic p-Laplace equation (2022)


Feng, Y., Parviainen, M., & Sarsa, S. (2022). On the second-order regularity of solutions to the parabolic p-Laplace equation. Journal of Evolution Equations, 22, Article 6. https://doi.org/10.1007/s00028-022-00760-3


JYU authors or editors


Publication details

All authors or editors: Feng, Yawen; Parviainen, Mikko; Sarsa, Saara

Journal or series: Journal of Evolution Equations

ISSN: 1424-3199

eISSN: 1424-3202

Publication year: 2022

Publication date: 26/02/2022

Volume: 22

Article number: 6

Publisher: Birkhäuser

Publication country: Switzerland

Publication language: English

DOI: https://doi.org/10.1007/s00028-022-00760-3

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/80280

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2110.07943


Abstract

In this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that D(|Du|p−2+s2Du) exists as a function and belongs to L2loc with s>−1 and 1

<∞. The range of s is sharp.


Keywords: partial differential equations

Free keywords: p-parabolic functions; weak solutions; fundamental inequality; Sobolev regularity; time derivative


Contributing organizations


Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 1


Last updated on 2024-22-04 at 15:48