A comparison principle for the porous medium equation and its consequences

Benny Avelin, Teemu Lukkari

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

We prove a comparison principle for the porous medium equation in more general open sets in ℝn+1 than space-time cylinders. We apply this result in two related contexts: we establish a connection between a potential theoretic notion of the obstacle problem and a notion based on a variational inequality. We also prove the basic properties of the PME capacity, in particular that there exists a capacitary extremal which gives the capacity for compact sets.

Original languageEnglish
Pages (from-to)573-594
Number of pages22
JournalRevista Matematica Iberoamericana
Volume33
Issue number2
DOIs
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Elliptic comparison principle
  • Obstacle problem
  • Parabolic capacity
  • PME
  • Porous medium equation

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