Lipschitz regularity for the parabolic $(s,p)-$obstacle problem

David Jesus; Aelson Sobral; José Miguel Urbano

Lipschitz regularity for the parabolic $(s,p)-$obstacle problem

Analysis of PDEs 2026-07-06 v1

Authors: David Jesus , Aelson Sobral , José Miguel Urbano

Abstract

We study the obstacle problem for the parabolic fractional $p-$ Laplace equation $\partial_t u+(-\Delta_p)^su = 0$ in the degenerate range $2<p<2/(1-s)$ . We prove that viscosity solutions are locally Lipschitz continuous in space and H\"older continuous in time. If, in addition, $p>1/(1-s)$ , the time regularity improves to Lipschitz continuity.

Cite

@article{arxiv.2607.04725,
  title  = {Lipschitz regularity for the parabolic $(s,p)-$obstacle problem},
  author = {David Jesus and Aelson Sobral and José Miguel Urbano},
  journal= {arXiv preprint arXiv:2607.04725},
  year   = {2026}
}