Weighted isoperimetric inequalities on ℝ n and applications to rearrangements

We study isoperimetric inequalities for a certain class of probability measures on ℝ n together with applications to integral inequalities for weighted rearrangements. Furthermore, we compare the solution to a linear elliptic problem with the solution to some “rearranged” problem defined in the domain { x : x 1 < α ( x 2 , …, x n )} with a suitable function α ( x 2 , …, x n ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)