JournalsjemsVol. 10 , No. 4DOI 10.4171/jems/142

Lieb–Thirring inequalities with improved constants

  • Ari Laptev

    Imperial College London, UK
  • Jean Dolbeault

    Université de Paris Dauphine, France
  • Michael Loss

    Georgia Institute of Technology, Atlanta, United States
Lieb–Thirring inequalities with improved constants cover

Abstract

Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multi-dimensional Schrödinger operators.