Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Transactions of the American Mathematical Society Année : 2018

Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities

Résumé

This paper deals with global dispersive properties of Schrödinger equations with realvalued potentials exhibiting critical singularities, where our class of potentials is more general than inverse-square type potentials and includes several anisotropic potentials. We first prove weighted resolvent estimates, which are uniform with respect to the energy, with a large class of weight functions in Morrey-Campanato spaces. Uniform Sobolev inequalities in Lorentz spaces are also studied. The proof employs the iterated resolvent identity and a classical multiplier technique. As an application, the full set of global-in-time Strichartz estimates including the endpoint case is derived. In the proof of Strichartz estimates, we develop a general criterion on perturbations ensuring that both homogeneous and inhomogeneous endpoint estimates can be recovered from resolvent estimates. Finally, we also investigate uniform resolvent estimates for long range repulsive potentials with critical singularities by using an elementary version of the Mourre theory.
Fichier principal
Vignette du fichier
critical-potential-2-2.pdf (290.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03376115 , version 1 (13-10-2021)

Identifiants

  • HAL Id : hal-03376115 , version 1

Citer

Jean-Marc Bouclet, Haruya Mizutani. Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities. Transactions of the American Mathematical Society, 2018. ⟨hal-03376115⟩
20 Consultations
105 Téléchargements

Partager

Gmail Facebook X LinkedIn More