Global higher integrability of weak solutions of porous medium systems

Kristian Moring, Christoph Scheven*, Sebastian Schwarzacher, Thomas Singer

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

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|m1u) = div F, where m > 1. More precisely, we prove that under suitable assumptions the spatial gradient D(|u|m1u) 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.

Original languageEnglish
Pages (from-to)1697-1745
Number of pages49
JournalCOMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Volume19
Issue number3
DOIs
Publication statusPublished - 1 Jan 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Gradient estimates
  • Higher integrability
  • Porous medium type systems

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