A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality
Analysis of PDEs
2017-11-17 v1
Abstract
We prove a Caffarelli--Kohn--Nirenberg inequality in the hyperbolic space. For a semilinear elliptic equation involving the associated weighted Laplace--Beltrami operator, we establish variationally the existence of positive radial solutions in the subcritical regime. We also show a non-existence result in star-shaped domains when the exponent is supercritical.
Keywords
Cite
@article{arxiv.1711.05927,
title = {A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality},
author = {Hardy Chan and Luiz Fernando de Oliveira Faria and Shaya Shakerian},
journal= {arXiv preprint arXiv:1711.05927},
year = {2017}
}