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

Pekka Koskela; Nageswari Shanmugalingam; Jeremy T. Tyson

doi:10.1023/B:POTA.0000033331.88514.6e

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

Pekka Koskela, Nageswari Shanmugalingam, Jeremy T. Tyson

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	241-262
Number of pages	22
Journal	Potential Analysis
Volume	21
Issue number	3
DOIs	https://doi.org/10.1023/B:POTA.0000033331.88514.6e
State	Published - Nov 2004

Keywords

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

ASJC Scopus subject areas

Analysis

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10.1023/B:POTA.0000033331.88514.6e

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abstract = "We answer a question of Jost on the validity of Poincar{\'e} 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.",

keywords = "Cheeger's differentiation theorem, Dirichlet forms, Doubling measure, Lipschitz function, Poincar{\'e} inequality, Sobolev space",

author = "Pekka Koskela and Nageswari Shanmugalingam and Tyson, {Jeremy T.}",

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AU - Tyson, Jeremy T.

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N2 - 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.

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KW - Doubling measure

KW - Lipschitz function

KW - Poincaré inequality

KW - Sobolev space

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

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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