On the second order regularity of solutions to the parabolic $p$-Laplace equation

Yawen Feng; Mikko Parviainen; Saara Sarsa

On the second order regularity of solutions to the parabolic $p$-Laplace equation

Analysis of PDEs 2021-10-18 v1

Authors: Yawen Feng , Mikko Parviainen , Saara Sarsa

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 $D(|Du|^{\frac{p-2+s}{2}}Du)$ exists as a function and belongs to $L^{2}_{\text{loc}}$ with $s>-1$ and $1<p<\infty$ . The range of $s$ is sharp.

Keywords

parabolic p-Laplace equation second order Sobolev regularity p-parabolic function sharp range

Cite

@article{arxiv.2110.07943,
  title  = {On the second order regularity of solutions to the parabolic $p$-Laplace equation},
  author = {Yawen Feng and Mikko Parviainen and Saara Sarsa},
  journal= {arXiv preprint arXiv:2110.07943},
  year   = {2021}
}

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