Interpolation inequalities and spectral estimates for magnetic operators

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Date
2017
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01534961
Dewey
Analyse
Sujet
Keller-Lieb-Thirring estimates; Gagliardo-Ni- renberg inequalities; spectral gap; optimal constants; Magnetic Laplacian; magnetic Schrödinger operator; logarithmic Sobolev inequalities; interpolation
URI
https://basepub.dauphine.fr/handle/123456789/17061
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Author
Dolbeault, Jean
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Esteban, Maria J.
4553 Department of Mathematics [Imperial College London]
Laptev, Ari
58807 Department of Mathematics Krasnoyarsk State University
Loss, Michael
7772 School of Mathematics - Georgia Institute of Technology
Type
Document de travail / Working paper
Item number of pages
24
Abstract (EN)
We prove magnetic interpolation inequalities and Keller-Lieb-Thir-ring estimates for the principal eigenvalue of magnetic Schrödinger operators. We establish explicit upper and lower bounds for the best constants and show by numerical methods that our theoretical estimates are accurate.