Conductor sobolev-type estimates and isocapacitary inequalities

Joan Cerdà, Joaquim Martín, Pilar Silvestre

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions.
Original languageEnglish
Pages (from-to)1925-1947
JournalIndiana University Mathematics Journal
Volume61
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

  • Convexity
  • Lower estimates
  • Rearrangement invariant spaces
  • Sobolev spaces
  • Sobolev-type inequalities

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