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