Characterizations of interior polar sets for the degenerate p-parabolic equation

Benny Avelin*, Olli Saari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This paper deals with different characterizations of sets of nonlinear parabolic capacity zero, with respect to the parabolic p-Laplace equation. Specifically we prove that certain interior polar sets can be characterized by sets of zero nonlinear parabolic capacity. Furthermore we prove that zero capacity sets are removable for bounded supersolutions and that sets of zero capacity have a relation to a certain parabolic Hausdorff measure.

Original languageEnglish
Pages (from-to)827–848
Number of pages22
JournalJournal of Evolution Equations
Volume17
Issue number2
DOIs
Publication statusPublished - Jun 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Characterization
  • Degenerate parabolic equations
  • Interior polar sets
  • Nonlinear potential theory
  • P-Laplace
  • P-parabolic equation
  • Parabolic capacity
  • Parabolic Hausdorff measure
  • Removability

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