On a class of weighted Gauss-type isoperimetric inequalities and   applications to symmetrization
  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. 
Michele Marini (SNS), Berardo Ruffini (IF)
math.AP