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

研究成果: Article

3 引用 (Scopus)

抄録

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 Hv s in the case 0 ≤ s < 3/2.

元の言語English
ページ(範囲)1993-2003
ページ数11
ジャーナルProceedings of the American Mathematical Society
133
発行部数7
DOI
出版物ステータスPublished - 2005 7
外部発表Yes

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Sobolev spaces
Singular Potential
Wave Operator
Lorentz Spaces
Homogeneous Space
Sobolev Spaces
Equivalence
Three-dimensional
Estimate

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

これを引用

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abstract = "We consider the Schr{\"o}dinger 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 Hv s in the case 0 ≤ s < 3/2.",
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AU - Ivanov, Angel

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N2 - 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 Hv s in the case 0 ≤ s < 3/2.

AB - 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 Hv s in the case 0 ≤ s < 3/2.

KW - Lorentz spaces

KW - Schrödinger equation

KW - Wave operators

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JF - Proceedings of the American Mathematical Society

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