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, MARIA FRANCESCA; F., Brock; Mercaldo, Anna; Posteraro, MARIA ROSARIA. - In: JOURNAL OF INEQUALITIES AND APPLICATIONS. - ISSN 1025-5834. - STAMPA. - 4:3(1999), pp. 215-240. [10.1155/S1025583499000375]
A weighted isoperimetric inequality and applications to symmetrization
BETTA, MARIA FRANCESCA;MERCALDO, ANNA;POSTERARO, MARIA ROSARIA
1999
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
