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.
1999
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/205338
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