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

### Michele Marini

Scuola Normale Superiore, Pisa, Italy### Berardo Ruffini

Université Grenoble I, Saint-Martin-d'Hères, France

## Abstract

We solve a class of weighted isoperimetric problems of the form

$\mathrm {min}\left\{\int_{\partial E}w e^V\,dx:\int_E e^V\,dx=\mathrm {constant}\right\}$

where $w$ and $V$ are suitable functions on $\mathbb R^d$. As a consequence, we prove a comparison result for the solutions of degenerate elliptic equations.

## Cite this article

Michele Marini, Berardo Ruffini, On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization. Rend. Sem. Mat. Univ. Padova 133 (2015), pp. 197–214

DOI 10.4171/RSMUP/133-10