On weighted isoperimetric inequalities with non-radial densities

2018/04/06 by Alvino, Angelo, Brock, Friedemann, Chiacchio, Francesco +2
#35P15 #46E30 #46E35 #51M16 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.02282

Abstract

We consider a class of isoperimetric problems on ℝ^N₊ where the volume and the area element carry two different weights of the type |x|^lx_N^α. We solve them in a special case while a more detailed study is contained in \citeABCMP2. Our results imply a weighted Polya-Szëgo principle and a priori estimates for weak solutions to a class of boundary value problems for degenerate elliptic equations

Related

• The isoperimetric problem for a class of non-radial weights and applications
• Some isoperimetric inequalities on ℝ ^N with respect to weights |x|^α
• On some Sobolev and Pólya-Szegö type inequalities with weights and applications
• On a class of weighted Gauss-type isoperimetric inequalities and applications to symmetrization
• An isoperimetric inequality for Gauss--like product measures