Isoperimetry and symmetrization for Sobolev spaces on metric spaces

Joaquim Martín; Mario Milman

doi:10.1016/j.crma.2009.04.011

Functional Analysis

Isoperimetry and symmetrization for Sobolev spaces on metric spaces
[Isopérimétrie et symetrisation dans des espaces de Sobolev sur les espaces métriques]

Présenté par : Gilles Pisier

Joaquim Martín ¹ ; Mario Milman ²

¹ Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
² Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431, USA

Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 627-630.

Résumé
Abstract

En utilisant l'isopérimétrie nous obtenons des nouvelles inégalités de symetrisation qui nous permettent de fournir un cadre unifié pour étudier des inégalités de Sobolev dans des espaces métriques. Les applications incluent des inégalités de concentration, inégalités de Poincaré, et des versions métriques des principes de Pólya–Szegö et de Faber–Krahn.

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.

Reçu le : 2008-06-16
Accepté le : 2009-04-08
Publié le : 2009-05-01

DOI : 10.1016/j.crma.2009.04.011

Affiliations des auteurs :

Joaquim Martín ¹ ; Mario Milman ²

¹ Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
² Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431, USA

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     author = {Joaquim Mart{\'\i}n and Mario Milman},
     title = {Isoperimetry and symmetrization for {Sobolev} spaces on metric spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {627--630},
     publisher = {Elsevier},
     volume = {347},
     number = {11-12},
     year = {2009},
     doi = {10.1016/j.crma.2009.04.011},
     language = {en},
}

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Joaquim Martín; Mario Milman. Isoperimetry and symmetrization for Sobolev spaces on metric spaces. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 627-630. doi : 10.1016/j.crma.2009.04.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.011/

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