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.
Accepted:
DOI: 10.1051/cocv/2017057
Keywords: multipolar, Hardy inequality, Riemannian manifolds
@article{COCV_2018__24_2_551_0, author = {Faraci, Francesca and Farkas, Csaba and Krist\'aly, Alexandru}, 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}, pages = {551--567}, publisher = {EDP-Sciences}, volume = {24}, number = {2}, year = {2018}, doi = {10.1051/cocv/2017057}, zbl = {1408.53052}, mrnumber = {3816404}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017057/} }
TY - JOUR AU - Faraci, Francesca AU - Farkas, Csaba AU - Kristály, Alexandru TI - Multipolar Hardy inequalities on Riemannian manifolds Dedicated to Professor Enrique Zuazua on the occasion of his 55th birthday JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 551 EP - 567 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017057/ DO - 10.1051/cocv/2017057 LA - en ID - COCV_2018__24_2_551_0 ER -
%0 Journal Article %A Faraci, Francesca %A Farkas, Csaba %A Kristály, Alexandru %T Multipolar Hardy inequalities on Riemannian manifolds Dedicated to Professor Enrique Zuazua on the occasion of his 55th birthday %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 551-567 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017057/ %R 10.1051/cocv/2017057 %G en %F COCV_2018__24_2_551_0
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, Volume 24 (2018) no. 2, pp. 551-567. doi : 10.1051/cocv/2017057. http://archive.numdam.org/articles/10.1051/cocv/2017057/
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