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Journal of Evolution Equations

, Volume 17, Issue 2, pp 827–848 | Cite as

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

  • Benny Avelin
  • Olli Saari
Article

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.

Keywords

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

Mathematics Subject Classification

Primary 35K92 Secondary 31C45 31C15 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Systems AnalysisAalto University School of ScienceAaltoFinland
  2. 2.Department of MathematicsUppsala UniversityUppsalaSweden

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