Multipolar Hardy inequalities on Riemannian manifolds: Dedicated to Professor Enrique Zuazua on the occasion of his 55th birthday

被引：0
|
作者：
Faraci F. [1 ]
Farkas C. [2 ]
Kristály A. [3 ]
机构：
[1] Department of Mathematics and Informatics, University of Catania
[2] Department of Mathematics and Informatics, Sapientia University, Tg. Mureş Romania, Institute of Applied Mathematics, Óbuda University, Budapest
[3] Department of Economics, Babeş-Bolyai University Cluj-Napoca, Romania, Institute of Applied Mathematics, Óbuda University, Budapest
来源：
Kristály, Alexandru (alex.kristaly@econ.ubbcluj.ro) | 2018年 / EDP Sciences卷 / 24期
关键词：
Hardy inequality; Multipolar; Riemannian manifolds;
D O I：
10.1051/cocv/2017057
中图分类号：
学科分类号：
摘要：
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. © EDP Sciences, SMAI 2018.
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页码：551 / 567
页数：16
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