Dispersive Estimates for the Schrödinger Equation with Potentials of Critical Regularity

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Abstract

We prove L1 → L∞ dispersive estimates with a logarithmic loss of derivatives for the Schrödinger group eit(−Δ+V) for a class of real-valued potentials V ∈ C(n−3)/2(â„›n), V(x) = O(〈x〉−δ), where n = 4, 5, Î´ > 3 if n = 4 and δ > 5 if n = 5.

Keywords

Schrödinger equation , dispersive estimates
  • 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.
  • Pages: 57–70
  • Date Published: 2009-12-01
  • Vol. 11 No. 5 (2009): CUBO, A Mathematical Journal

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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.

Issue

Vol. 11 No. 5 (2009): CUBO, A Mathematical Journal

Section

Articles