Multipolar Hardy inequalities on Riemannian manifolds Dedicated to Professor Enrique Zuazua on the occasion of his 55th birthday
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 551-567.

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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017057
Classification : 53C21, 35J10, 35J20
Mots clés : multipolar, Hardy inequality, Riemannian manifolds
Faraci, Francesca 1 ; Farkas, Csaba 1 ; Kristály, Alexandru 1

1
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     title = {Multipolar {Hardy} inequalities on {Riemannian} manifolds {Dedicated} to {Professor} {Enrique} {Zuazua} on the occasion of his 55th birthday},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Faraci, Francesca; Farkas, Csaba; Kristály, Alexandru. Multipolar Hardy inequalities on Riemannian manifolds Dedicated to Professor Enrique Zuazua on the occasion of his 55th birthday. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 551-567. doi : 10.1051/cocv/2017057. http://www.numdam.org/articles/10.1051/cocv/2017057/

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