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

Michele Marini (1) , Berardo Ruffini (2)

1 SNS - Scuola Normale Superiore di Pisa
2 IF - Institut Fourier

We solve a class of weighted isoperimetric problems of the form min{\int_{\partial E} we^V dx : \int_E eV dx=constant} where w and V are suitable functions on R^N. As a consequence, we prove a comparison result for the solutions of degenerate elliptic equations.

Domaines: Equations aux dérivées partielles [math.AP]

Michele Marini, Berardo Ruffini. On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization. 2014. ⟨hal-00941120v1⟩