On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization

Michele Marini; Berardo Ruffini

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arXiv · 1402.0470

On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization

Michele Marini·Berardo Ruffini

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Abstract

We solve a class of weighted isoperimetric problems of the form $$ \min\left\{\int\_{\partial E}w e^V\,dx:\int\_E e^V\,dx={\rm constant}\right\} $$ where $w$ and $V$ are suitable functions on $\R^d$. As a consequence, we prove a comparison result for the solutions of degenerate elliptic equations.

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Michele Marini, Berardo Ruffini. 2014-02-03. On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization. https://arxiv.org/abs/1402.0470

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