Parabolic Capacity and Soft Measures for Nonlinear Equations

Jérôme Droniou, Alessio Porretta, Alain Prignet

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70 Citations (Scopus)

Abstract

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.

Original languageEnglish
Pages (from-to)99-161
Number of pages63
JournalPotential Analysis
Volume19
Issue number2
DOIs
Publication statusPublished - 1 Sep 2003
Externally publishedYes

Keywords

  • Capacity
  • Measure
  • Parabolic equations

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