Issue |
ESAIM: COCV
Volume 24, Number 2, April–June 2018
|
|
---|---|---|
Page(s) | 551 - 567 | |
DOI | https://doi.org/10.1051/cocv/2017057 | |
Published online | 26 January 2018 |
Multipolar Hardy inequalities on Riemannian manifolds
Dedicated to Professor Enrique Zuazua on the occasion of his 55th birthday
1
Department of Mathematics and Informatics, University of Catania, Italy
ffaraci@dmi.unict.it
2
Department of Mathematics and Informatics, Sapientia University, Tg. Mureş, Romania, Institute of Applied Mathematics, Óbuda University,
1034,
Budapest, Hungary
farkas.csaba2008@gmail.com; farkascs@ms.sapientia.ro
3
Department of Economics, Babeş-Bolyai University, Cluj-Napoca, Romania, Institute of Applied Mathematics, Óbuda University,
1034,
Budapest, Hungary
alex.kristaly@econ.ubbcluj.ro
a Corresponding author: alexandrukristaly@yahoo.com
Received:
26
January
2017
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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