Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems
Mathematical Physics
2007-05-23 v1 Analysis of PDEs
Functional Analysis
math.MP
Abstract
We prove a Lieb-Thirring type inequality for potentials such that the associated Schr\"{o}dinger operator has a pure discrete spectrum made of an unbounded sequence of eigenvalues. This inequality is equivalent to a generalized Gagliardo-Nirenberg inequality for systems. As a special case, we prove a logarithmic Sobolev inequality for infinite systems of mixed states. Optimal constants are determined and free energy estimates in connection with mixed states representations are also investigated.
Keywords
Cite
@article{arxiv.math-ph/0506052,
title = {Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems},
author = {Jean Dolbeault and Patricio Felmer and Michael Loss and Eric Paturel},
journal= {arXiv preprint arXiv:math-ph/0506052},
year = {2007}
}