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Annales Henri Poincaré

, Volume 19, Issue 5, pp 1439–1463 | Cite as

Interpolation Inequalities and Spectral Estimates for Magnetic Operators

  • Jean Dolbeault
  • Maria J. Esteban
  • Ari Laptev
  • Michael Loss
Article

Abstract

We prove magnetic interpolation inequalities and Keller–Lieb–Thirring 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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jean Dolbeault
    • 1
  • Maria J. Esteban
    • 1
  • Ari Laptev
    • 2
    • 3
  • Michael Loss
    • 4
  1. 1.CEREMADE (CNRS UMR no 7534)PSL Research University, Université Paris-DauphineParis 16France
  2. 2.Department of MathematicsImperial College LondonLondonUK
  3. 3.Department of MathematicsSiberian Federal UniversityKrasnoyarskRussia
  4. 4.School of Mathematics, Skiles BuildingGeorgia Institute of TechnologyAtlantaUSA

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