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arXiv · 1609.01080

Multipolar Hardy inequalities on Riemannian manifolds

Francesca Faraci·Csaba Farkas·Alexandru Kristály
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Abstract

We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [Improved multipolar Hardy inequalities, 2013]. We notice that our inequalities deeply depend on the curvature, providing (quantitative) information about the deflection from the flat case. By using these inequalities together with variational methods and group-theoretical arguments, we also establish non-existence, existence and multiplicity results for certain Schr\"odinger-type problems involving the Laplace-Beltrami operator and bipolar potentials on Cartan-Hadamard manifolds and on the open upper hemisphere, respectively.

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Francesca Faraci, Csaba Farkas, Alexandru Kristály. 2016-09-05. Multipolar Hardy inequalities on Riemannian manifolds. https://arxiv.org/abs/1609.01080

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