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arXiv · 1504.04961

An isoperimetric inequality for Gauss--like product measures

Friedemann Brock·Francesco Chiacchio·Anna Mercaldo
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Abstract

This paper deals with various questions related to the isoperimetic problem for smooth positive measure $d\mu = \varphi(x)dx$, with $x \in \Omega \subset \mathbb{R}^N$. Firstly we find some necessary conditions on the density of the measure $ \varphi(x)$ that render the intersection of half spaces with $\Omega$ a minimum in the isoperimetric problem. We then identify the unique isoperimetric set for a wide class of factorized finite measures. These results are finally used in order to get sharp inequalities in weighted Sobolev spaces and a comparison result for solutions to boundary value problems for degenerate elliptic equations.

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Friedemann Brock, Francesco Chiacchio, Anna Mercaldo. 2015-04-20. An isoperimetric inequality for Gauss--like product measures. https://arxiv.org/abs/1504.04961

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