%0 Journal Article
%T On isoperimetric inequalities with respect to infinite measures
%A F. Brock
%A A. Mercaldo
%A M. R. Posteraro
%J Mathematics
%D 2011
%I arXiv
%X We study isoperimetric problems with respect to infinite measures on $R ^n$. In the case of the measure $\mu$ defined by $d\mu = e^{c|x|^2} dx$, $c\geq 0$, we prove that, among all sets with given $\mu-$measure, the ball centered at the origin has the smallest (weighted) $\mu-$perimeter. Our results are then applied to obtain Polya-Szego-type inequalities, Sobolev embeddings theorems and a comparison result for elliptic boundary value problems.
%U http://arxiv.org/abs/1108.0863v1