Inequalities involving Aharonov-Bohm magnetic potentials in dimensions 2 and 3

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Date
2019Publisher city
ParisPublisher
Cahier de recherche CEREMADE, Université Paris-DauphinePublishing date
02-2019Collection title
Cahier de recherche CEREMADE, Université Paris-DauphineLink to item file
https://hal.archives-ouvertes.fr/hal-02021174Dewey
AnalyseSujet
Aharonov-Bohm magnetic potential; radial symmetry; cylindrical symmetry; symmetry breaking; magnetic Hardy inequality; magnetic interpolation inequality; optimal constants; magnetic Schrödinger operator; magnetic Keller-Lieb-Thirring inequality; magnetic ringsCollections
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Bonheure, Denis
255058 Département de mathématiques Université Libre de Bruxelles
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Esteban, Maria J.
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laptev, Ari
4553 Department of Mathematics [Imperial College London]
Loss, Michael
7772 School of Mathematics - Georgia Institute of Technology
Type
Item number of pages
25Abstract (EN)
This paper is devoted to interpolation inequalities of Gagliardo-Nirenberg type associated with Schrödinger operators involving Aharonov-Bohm magnetic potentials and related magnetic Hardy inequalities in dimensions 2 and 3. The focus is on symmetry properties of the optimal functions, with explicit ranges of symmetry and symmetry breaking in terms of the intensity of the magnetic potential.Related items
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