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

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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Hauptverfasser: Chan, Hardy, Faria, Luiz Fernando de Oliveira, Shakerian, Shaya
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Analysis of PDEs
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Zusammenfassung: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