Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Functional Analysis Année : 2006

Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems

Résumé

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.

Dates et versions

hal-00005487 , version 1 (07-11-2005)

Identifiants

Citer

Jean Dolbeault, Patricio Felmer, Michael Loss, Eric Paturel. Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems. Journal of Functional Analysis, 2006, 238 (1), pp.193-220. ⟨hal-00005487⟩
219 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More