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

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Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
02-2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02021174
Dewey
Analyse
Sujet
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 rings
URI
https://basepub.dauphine.fr/handle/123456789/18551
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Author
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
Document de travail / Working paper
Item number of pages
25
Abstract (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.