Volume 24, Number 2, April–June 2018
|Page(s)||551 - 567|
|Published online||26 January 2018|
Multipolar Hardy inequalities on Riemannian manifolds
Dedicated to Professor Enrique Zuazua on the occasion of his 55th birthday
Department of Mathematics and Informatics, University of Catania, Italy
2 Department of Mathematics and Informatics, Sapientia University, Tg. Mureş, Romania, Institute of Applied Mathematics, Óbuda University, 1034, Budapest, Hungary
3 Department of Economics, Babeş-Bolyai University, Cluj-Napoca, Romania, Institute of Applied Mathematics, Óbuda University, 1034, Budapest, Hungary
a Corresponding author: firstname.lastname@example.org
Revised: 8 July 2017
Accepted: 26 August 2017
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 Schrödinger-type problems involving the Laplace-Beltrami operator and bipolar potentials on Cartan-Hadamard manifolds and on the open upper hemisphere, respectively.
Mathematics Subject Classification: 53C21 / 35J10 / 35J20
Key words: multipolar / Hardy inequality / Riemannian manifolds
© EDP Sciences, SMAI 2018
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