10/8/2007

Rupert Frank
Princeton University

Hardy-Sobolev and Lieb-Thirring inequalities

We consider the relation between inequalities on eigenvalue moments of Schr\"odinger-like operators and Sobolev-like inequalities. We present some new Hardy-Sobolev inequalities for the Laplacian in a convex domain and for fractional powers of the Laplacian. As a consequence we deduce that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schr\"odinger-like operators remain true, with possibly different constants, when the critical Hardy-weight is subtracted from the Laplace operator.

The talk is based on joint work with E.H. Lieb and R. Seiringer. .