Proceedings of the American Mathematical Society

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

Author(s): Vladimir Georgiev; Angel Ivanov
Journal: Proc. Amer. Math. Soc. 133 (2005), 1993-2003.
MSC (2000): Primary 35J10, 35P25, 35B45
Posted: February 15, 2005
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Abstract: We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space $L^{3/2,\infty}$ 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 $\dot{H}^s$ and $\dot{H}^s_V$ in the case $0 \leq s < \frac{3}{2}$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J10, 35P25, 35B45

Vladimir Georgiev
Affiliation: Dipartimento di Matematica, Università di Pisa, Via Buonarroti No.2, 56127 - Pisa, Italy
Email: georgiev@dm.unipi.it

Angel Ivanov
Affiliation: Dipartimento di Matematica, Università di Pisa, Via Buonarroti No.2, 56127 - Pisa, Italy
Email: ivanov@mail.dm.unipi.it

DOI: 10.1090/S0002-9939-05-07854-8
PII: S 0002-9939(05)07854-8
Keywords: Schr\"{o}dinger equation, Lorentz spaces, wave operators
Received by editor(s): February 16, 2004
Posted: February 15, 2005
Additional Notes: The authors were partially supported by the Research Training Network (RTN) HYKE, financed by the European Union, contract number: HPRN-CT-2002-00282.
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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