Comptes Rendus
no. 11-12
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 Martín1 ; Mario Milman2
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.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.04.011
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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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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