Parabolic Capacity and Soft Measures for Nonlinear Equations

Jérôme Droniou, Alessio Porretta, Alain Prignet

Research output: Contribution to journalArticleResearchpeer-review

98 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1 Sept 2003
Externally publishedYes


  • Capacity
  • Measure
  • Parabolic equations

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