Interpolation inequalities and spectral estimates for magnetic operators

Jean Dolbeault (1) , Maria J. Esteban (1) , Ari Laptev (2) , Michael Loss (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics [Imperial College London]
3 School of Mathematics - Georgia Institute of Technology

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.

Mots clés: Gagliardo-Nirenberg inequalities; spectral gap; magnetic Schrödinger operator; Magnetic Laplacian; logarithmic Sobolev inequalities; Keller-Lieb-Thirring estimates; interpolation; optimal constants

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Jean Dolbeault, Maria J. Esteban, Ari Laptev, Michael Loss. Interpolation inequalities and spectral estimates for magnetic operators. Annales Henri Poincaré. A Journal of Theoretical and Mathematical Physics, 2018, 19 (5), pp.1439-1463. ⟨10.1007/s00023-018-0663-9⟩. ⟨hal-01534961v2⟩