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Interpolation inequalities and spectral estimates for magnetic operators

Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael (2018), Interpolation inequalities and spectral estimates for magnetic operators, Annales Henri Poincaré, 19, p. 1439–1463. https://doi.org/10.1007/s00023-018-0663-9

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Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01534961
Date
2018
Journal name
Annales Henri Poincaré
Volume
19
Pages
1439–1463
Publication identifier
Metadata
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Author(s)
Dolbeault, Jean cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Esteban, Maria J. cc
Department of Mathematics [Imperial College London]
Laptev, Ari
Department of Mathematics Krasnoyarsk State University
Loss, Michael
School of Mathematics - Georgia Institute of Technology
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.
Subjects / Keywords
Keller-Lieb-Thirring estimates; Gagliardo-Ni- renberg inequalities; spectral gap; optimal constants; Magnetic Laplacian; magnetic Schrödinger operator; logarithmic Sobolev inequalities; interpolation