Isoperimetry and Symmetrization for Sobolev spaces on metric spaces

Details Isoperimetry and Symmetrization for Sobolev spaces on metric spaces Isoperimetry and Symmetrization for Sobolev spaces on metric spaces

2008-06-18

arxiv.org/abs/0806.3053v2

C. R. Acad. Sci. I (2009)

Mathematics

Functional Analysis

corrected version

Scientific paper

10.1016/j.crma.2009.04.01

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, as well as metric versions of
the P\'{o}% lya-Szeg\"{o} and Faber-Krahn principles.

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