Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation

Juha Kinnunen*, Peter Lindqvist

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

56 Citations (Scopus)

Abstract

A kind of supersolutions of the so-called p-parabolic equation are studied. These p-superparabolic functions are defined as lower semicontinuous functions obeying the comparison principle. Incidentally, they are precisely the viscosity supersolutions. One of our results guarantees the existence of a spatial Sobolev gradient. For p = 2 we have the supercaloric functions and the ordinary heat equation.

Original languageEnglish
Pages (from-to)411-435
Number of pages25
JournalAnnali di Matematica Pura ed Applicata
Volume185
Issue number3
DOIs
Publication statusPublished - Aug 2006
MoE publication typeA1 Journal article-refereed

Keywords

  • Comparison principle
  • Obstacle problem
  • Parabolic p-Laplace equation

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