We prove an inequality of the form integral(partial derivative Omega) a(\x)Hn-1 (dx) greater than or equal to integral(partial derivative B) a()Hn-1 (dx), where Omega is a bounded domain in R-n with smooth boundary, B is a ball centered in the origin having the same measure as Omega. From this we derive inequalities comparing a weighted Sobolev norm of a given function with the norm of its symmetric decreasing rearrangement. Furthermore, we use the inequality to obtain comparison results for elliptic boundary value problems.
A weighted isoperimetric inequality and applications to symmetrization
Betta, MF;
1999-01-01
Abstract
We prove an inequality of the form integral(partial derivative Omega) a(\x)Hn-1 (dx) greater than or equal to integral(partial derivative B) a()Hn-1 (dx), where Omega is a bounded domain in R-n with smooth boundary, B is a ball centered in the origin having the same measure as Omega. From this we derive inequalities comparing a weighted Sobolev norm of a given function with the norm of its symmetric decreasing rearrangement. Furthermore, we use the inequality to obtain comparison results for elliptic boundary value problems.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
