Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Vladimir Georgiev and Angel Ivanov
Journal: Proc. Amer. Math. Soc. 133 (2005), 1993-2003
MSC (2000): Primary 35J10, 35P25, 35B45
Published electronically: February 15, 2005
MathSciNet review: 2137865
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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} $.


References [Enhancements On Off] (What's this?)


Similar Articles

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

Retrieve articles in all journals with MSC (2000): 35J10, 35P25, 35B45


Additional Information

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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.