English

Optimal regularity in time and space for the porous medium equation

Analysis of PDEs 2020-12-30 v1

Abstract

Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that these estimates are optimal. In the linear limit, the proven regularity estimates are consistent with the optimal regularity of the linear case.

Keywords

Cite

@article{arxiv.1902.08632,
  title  = {Optimal regularity in time and space for the porous medium equation},
  author = {Benjamin Gess and Jonas Sauer and Eitan Tadmor},
  journal= {arXiv preprint arXiv:1902.08632},
  year   = {2020}
}

Comments

36 pages

R2 v1 2026-06-23T07:48:31.401Z