Isoperimetry and symmetrization for Sobolev spaces on metric spaces

Joaquim Martín; Mario Milman

doi:https://doi.org/10.1016/j.crma.2009.04.011

Isoperimetry and symmetrization for Sobolev spaces on metric spaces

Joaquim Martín, Mario Milman

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

Abstract

Using isoperimetry we obtain new symmetrization inequalities that allow us to provide a unified framework to study Sobolev inequalities in metric spaces. The applications include concentration inequalities, Poincaré inequalities, as well as metric versions of the Pólya-Szegö and Faber-Krahn principles. To cite this article: J. Martín, M. Milman, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.

Original language	English
Pages (from-to)	627-630
Journal	Comptes Rendus Mathematique
Volume	347
DOIs	https://doi.org/10.1016/j.crma.2009.04.011
Publication status	Published - 1 Jun 2009

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title = "Isoperimetry and symmetrization for Sobolev spaces on metric spaces",

abstract = "Using isoperimetry we obtain new symmetrization inequalities that allow us to provide a unified framework to study Sobolev inequalities in metric spaces. The applications include concentration inequalities, Poincar{\'e} inequalities, as well as metric versions of the P{\'o}lya-Szeg{\"o} and Faber-Krahn principles. To cite this article: J. Mart{\'i}n, M. Milman, C. R. Acad. Sci. Paris, Ser. I 347 (2009). {\textcopyright} 2009 Acad{\'e}mie des sciences.",

author = "Joaquim Mart{\'i}n and Mario Milman",

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AU - Milman, Mario

PY - 2009/6/1

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N2 - Using isoperimetry we obtain new symmetrization inequalities that allow us to provide a unified framework to study Sobolev inequalities in metric spaces. The applications include concentration inequalities, Poincaré inequalities, as well as metric versions of the Pólya-Szegö and Faber-Krahn principles. To cite this article: J. Martín, M. Milman, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.

AB - Using isoperimetry we obtain new symmetrization inequalities that allow us to provide a unified framework to study Sobolev inequalities in metric spaces. The applications include concentration inequalities, Poincaré inequalities, as well as metric versions of the Pólya-Szegö and Faber-Krahn principles. To cite this article: J. Martín, M. Milman, C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.

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DO - https://doi.org/10.1016/j.crma.2009.04.011

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EP - 630

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JF - Comptes Rendus Mathematique

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