On weighted isoperimetric inequalities with non-radial densities

We consider a class of isoperimetric problems on , where the volume and the area element carry two different weights of the type . We solve them in a special case while a more detailed study is contained in Alvino et al. (The isoperimetric problem for a class of non-radial weights and applications,...

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Published inApplicable analysis Vol. 98; no. 10; pp. 1935 - 1945
Main Authors Alvino, A., Brock, F., Chiacchio, F., Mercaldo, A., Posteraro, M. R.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 27.07.2019
Taylor & Francis Ltd
Subjects
Boundary value problems
elliptic boundary value problem
Elliptic functions
Isoperimetric inequality
Isoperimetric problem
norm inequality
weighted rearrangement
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Summary:We consider a class of isoperimetric problems on , where the volume and the area element carry two different weights of the type . We solve them in a special case while a more detailed study is contained in Alvino et al. (The isoperimetric problem for a class of non-radial weights and applications, in preparation). Our results imply a weighted Pólya-Szëgo principle and a priori estimates for weak solutions to a class of boundary value problems for degenerate elliptic equations.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2018.1506106