Dispersive Estimates for the Schrödinger Equation with Potentials of Critical Regularity

Fernando Cardoso; Claudio Cuevas; Georgi Vodev

Dispersive Estimates for the Schrödinger Equation with Potentials of Critical Regularity

Authors

Fernando Cardoso Universidade Federal de Pernambuco, Departamento de Matemática, CEP. 50540-740 Recife-Pe, Brazil.
Claudio Cuevas Universidade Federal de Pernambuco, Departamento de Matemática, CEP. 50540-740 Recife-Pe, Brazil.
Georgi Vodev Département de Mathématiques, UMR 6629 du CNRS, Université de Nantes, 2 rue de la Houssinière, BP 92208, FR-44322 Nantes Cedex 03, France.

Keywords:

Schrödinger equation, dispersive estimates

Abstract

We prove L¹ â†’ L^âˆž dispersive estimates with a logarithmic loss of derivatives for the Schrödinger group e^it^{(âˆ’Î”+V)} for a class of real-valued potentials V âˆˆ C^{(nâˆ’3)/2}(â„›ⁿ), V(x) = O(âŒ©xâŒª^âˆ’Î´), where n = 4, 5, Î´ > 3 if n = 4 and Î´ > 5 if n = 5.

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Published

2009-12-01

How to Cite

[1]

F. Cardoso, C. Cuevas, and G. Vodev, “Dispersive Estimates for the Schrödinger Equation with Potentials of Critical Regularity”, CUBO, vol. 11, no. 5, pp. 57–70, Dec. 2009.