Dispersive estimates for the Schrödinger equation in dimensions four and five

Article type: Research Article

Authors: Cardoso, Fernando | Cuevas, Claudio | Vodev, Georgi^;

Affiliations: Universidade Federal de Pernambuco, Departamento de Matemática, CEP. 50540-740 Recife-Pe, Brazil | Université de Nantes, Département de Mathématiques, UMR 6629 du CNRS, 2, rue de la Houssinière, BP 92208, 44332 Nantes Cedex 03, France. E-mail: [email protected]

Note: [] Corresponding author.

Abstract: We prove optimal (that is, without loss of derivatives) dispersive estimates for the Schrödinger group eit(−Δ+V) for a class of real-valued potentials V∈Ck(Rn), V(x)=O(〈x〉−δ), where n=4, 5, k>(n−3)/2, δ>3 if n=4 and δ>5 if n=5.

Keywords: Schrödinger equation, potential, dispersive estimates

DOI: 10.3233/ASY-2009-0916

Journal: Asymptotic Analysis, vol. 62, no. 3-4, pp. 125-145, 2009