English

On weighted isoperimetric inequalities with non-radial densities

Analysis of PDEs 2018-04-09 v1

Abstract

We consider a class of isoperimetric problems on R+N\mathbb{R}^{N}_{+} where the volume and the area element carry two different weights of the type xlxNα|x|^lx_N^\alpha. We solve them in a special case while a more detailed study is contained in \cite{ABCMP2}. Our results imply a weighted Polya-Sz\"ego principle and a priori estimates for weak solutions to a class of boundary value problems for degenerate elliptic equations

Keywords

Cite

@article{arxiv.1804.02282,
  title  = {On weighted isoperimetric inequalities with non-radial densities},
  author = {Angelo Alvino and Friedemann Brock and Francesco Chiacchio and Anna Mercaldo and Maria Rosaria Posteraro},
  journal= {arXiv preprint arXiv:1804.02282},
  year   = {2018}
}