Lower semicontinuous obstacles for the porous medium equation

Riikka Korte*, Pekka Lehtelä, Stefan Sturm

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
48 Downloads (Pure)


We deal with the obstacle problem for the porous medium equation in the slow diffusion regime m>1. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered obstacles are not regular enough to work with the classical notion of variational solutions, and a different approach is needed. We prove the existence of a solution in the sense of the minimal supersolution lying above the obstacle. As a consequence, we can show that non-negative weak supersolutions to the porous medium equation can be approximated by a sequence of supersolutions which are bounded away from zero.

Original languageEnglish
Pages (from-to)1851-1864
Number of pages14
JournalJournal of Differential Equations
Issue number4
Publication statusPublished - 5 Feb 2019
MoE publication typeA1 Journal article-refereed


  • Irregular obstacles
  • Obstacle problem
  • Porous medium equation


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