Resumen de Lieb-Thirring inequalities with improved constants

Jean Dolbeault, Ari Laptev, Michael Loss

• 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