Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : We prove a Lieb-Thirring type inequality for potentials such that the associated Schrödinger 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.
 
 
Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems
DOLBEAULT Jean, FELMER Patricio, LOSS Michael
PATUREL Eric
2005-27
23-06-2005
 
Université de PARIS - DAUPHINE
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