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arXiv · 1711.05927

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

Hardy Chan·Luiz Fernando de Oliveira Faria·Shaya Shakerian
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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.

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Hardy Chan, Luiz Fernando de Oliveira Faria, Shaya Shakerian. 2017-11-16. A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality. https://arxiv.org/abs/1711.05927

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