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Weighted isoperimetric inequalities on ℝ n and applications to rearrangements
Author(s) -
Betta M. Francesca,
Brock Friedemann,
Mercaldo Anna,
Posteraro M. Rosaria
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510619
Subject(s) - isoperimetric inequality , mathematics , domain (mathematical analysis) , inequality , class (philosophy) , combinatorics , pure mathematics , function (biology) , mathematical analysis , computer science , artificial intelligence , evolutionary biology , biology
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)