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Interpolation Inequalities and Spectral Estimates for Magnetic Operators

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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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Authors and Affiliations

  1. CEREMADE (CNRS UMR no 7534), PSL Research University, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris 16, France

    Jean Dolbeault & Maria J. Esteban

  2. Department of Mathematics, Imperial College London, Huxley Building, 180 Queen’s Gate, London, SW7 2AZ, UK

    Ari Laptev

  3. Department of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

    Ari Laptev

  4. School of Mathematics, Skiles Building, Georgia Institute of Technology, Atlanta, GA , 30332-0160, USA

    Michael Loss

Authors
  1. Jean Dolbeault
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  2. Maria J. Esteban
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  3. Ari Laptev
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  4. Michael Loss
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Corresponding author

Correspondence to Jean Dolbeault.

Additional information

Communicated by Jan Dereziński.

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Dolbeault, J., Esteban, M.J., Laptev, A. et al. Interpolation Inequalities and Spectral Estimates for Magnetic Operators. Ann. Henri Poincaré 19, 1439–1463 (2018). https://doi.org/10.1007/s00023-018-0663-9

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  • DOI: https://doi.org/10.1007/s00023-018-0663-9

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