Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential

Vladimir Georgiev, Angel Ivanov

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space L3/2,∞ and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces Hs and Hvs in the case 0 ≤ s < 3/2.

Original languageEnglish
Pages (from-to)1993-2003
Number of pages11
JournalProceedings of the American Mathematical Society
Volume133
Issue number7
DOIs
Publication statusPublished - 2005 Jul 1
Externally publishedYes

Keywords

  • Lorentz spaces
  • Schrödinger equation
  • Wave operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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