Optimal regularity in time and space for the porous medium equation

Benjamin Gess; Jonas Sauer; Eitan Tadmor

doi:10.2140/apde.2020.13.2441

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.

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Benjamin Gess. Jonas Sauer. Eitan Tadmor. "Optimal regularity in time and space for the porous medium equation." Anal. PDE 13 (8) 2441 - 2480, 2020. https://doi.org/10.2140/apde.2020.13.2441

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Received: 19 April 2019; Revised: 30 July 2019; Accepted: 26 September 2019; Published: 2020

First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.2140/apde.2020.13.2441

Subjects:

Primary: 35B65 , 35D30 , 35K59 , 76S05

Keywords: entropy solutions , kinetic formulation , porous medium equation , regularity results , velocity averaging

Abstract

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