A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality

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 re...

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Bibliographic Details
Main Authors Chan, Hardy, Faria, Luiz Fernando de Oliveira, Shakerian, Shaya
Format Journal Article
LanguageEnglish
Published 16.11.2017
Subjects
Mathematics - Analysis of PDEs
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Summary: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.
DOI:10.48550/arxiv.1711.05927