Higher integrability for the singular porous medium system

Bögelein V, Duzaar F, Scheven C (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Journal für die reine und angewandte Mathematik Walter de Gruyter

Pages Range: 203-230

Journal Issue: 767

URI: https://www.degruyter.com/document/doi/10.1515/crelle-2019-0038/html

DOI: 10.1515/crelle-2019-0038

Abstract

In this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse Hölder inequality for the gradient. The novel feature in the proof is a suitable intrinsic scaling for space-time cylinders combined with reverse Hölder inequalities and a Vitali covering argument within this geometry. The main result holds for the natural range of parameters suggested by other regularity results. Our result applies to general fast diffusion systems and includes both, non-negative and signed solutions in the case of equations. The methods of proof are purely vectorial in their structure.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT) Universität Duisburg-Essen (UDE) DE Germany (DE)

How to cite

APA:

Bögelein, V., Duzaar, F., & Scheven, C. (2019). Higher integrability for the singular porous medium system. Journal für die reine und angewandte Mathematik, 767, 203-230. https://dx.doi.org/10.1515/crelle-2019-0038

MLA:

Bögelein, Verena, Frank Duzaar, and Christoph Scheven. "Higher integrability for the singular porous medium system." Journal für die reine und angewandte Mathematik 767 (2019): 203-230.

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