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.
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.
Accepted:
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Joaquim Martín 1; Mario Milman 2
@article{CRMATH_2009__347_11-12_627_0, 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}, }
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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