Equivalence of Sobolev Inequalities and Lieb-Thirring Inequalities
Abstract
We show that, under very general definitions of a kinetic energy operator T, the Lieb-Thirring inequalities for sums of eigenvalues of T - V can be derived from the Sobolev inequality appropriate to that choice of T.
- Publication:
-
XVITH INTERNATIONAL CONGRESS ON MATHEMATICAL PHYSICS. Held 3-8 August 2009 in Prague
- Pub Date:
- March 2010
- DOI:
- 10.1142/9789814304634_0045
- arXiv:
- arXiv:0909.5449
- Bibcode:
- 2010maph.conf..523F
- Keywords:
-
- Schrödinger operator;
- Sobolev inequality;
- bound states;
- stability of matter;
- Mathematics - Spectral Theory;
- Mathematical Physics
- E-Print:
- 13 pages