Global higher integrability of weak solutions of porous medium systems

Moring K, Scheven C, Schwarzacher S, Singer T (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Communications on Pure and Applied Analysis American Institute of Mathematical Sciences (AIMS)

Book Volume: 19

Pages Range: 1697-1745

Journal Issue: 3

DOI: 10.3934/cpaa.2020069

Abstract

We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by ∂tu − ∆(|u|m−1u) = div F, where m > 1. More precisely, we prove that under suitable assumptions the spatial gradient D(|u|m−1u) of any weak solution is integrable to a larger power than the natural power 2. Our analysis includes both the case of the lateral boundary and the initial boundary.

Authors with CRIS profile

Thomas Singer Department Mathematik

Involved external institutions

Aalto University Espoo FI Finland (FI) Universität Duisburg-Essen (UDE) DE Germany (DE) Univerzita Karlova v Praze / Charles University in Prague CZ Czech Republic (CZ)

How to cite

APA:

Moring, K., Scheven, C., Schwarzacher, S., & Singer, T. (2020). Global higher integrability of weak solutions of porous medium systems. Communications on Pure and Applied Analysis, 19(3), 1697-1745. https://dx.doi.org/10.3934/cpaa.2020069

MLA:

Moring, Kristian, et al. "Global higher integrability of weak solutions of porous medium systems." Communications on Pure and Applied Analysis 19.3 (2020): 1697-1745.

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