Dirichlet forms, Poincaré inequalities, and the Sobolev spaces of Korevaar and Schoen

Pekka Koskela, Nageswari Shanmugalingam, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

Abstract

We answer a question of Jost on the validity of Poincaré inequalities for metric space-valued functions in a Dirichlet domain. We also investigate the relationship between Dirichlet domains and the Sobolev-type spaces introduced by Korevaar and Schoen.

Original languageEnglish (US)
Pages (from-to)241-262
Number of pages22
JournalPotential Analysis
Volume21
Issue number3
DOIs
StatePublished - Nov 1 2004

Keywords

  • Cheeger's differentiation theorem
  • Dirichlet forms
  • Doubling measure
  • Lipschitz function
  • Poincaré inequality
  • Sobolev space

ASJC Scopus subject areas

  • Analysis

Fingerprint Dive into the research topics of 'Dirichlet forms, Poincaré inequalities, and the Sobolev spaces of Korevaar and Schoen'. Together they form a unique fingerprint.

Cite this