Advances in Differential Equations

Uniqueness theorem in weighted Sobolev spaces of the Cauchy problem for Schrödinger type equations with variable coefficients

Yuya Dan

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Abstract

The present paper is concerned with the uniqueness of solutions to the Cauchy problem for the Schrödinger type equations with variable coefficients. It is proved by the wellposedness of the associated adjoint problem that there is a unique solution to the Cauchy problem in exponentially weighted Sobolev spaces. The result, in this paper, is a natural generalization of that in the previous work.

Article information

Source
Adv. Differential Equations Volume 13, Number 5-6 (2008), 489-507.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867343

Mathematical Reviews number (MathSciNet)
MR2482396

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics
Secondary: 35A02: Uniqueness problems: global uniqueness, local uniqueness, non- uniqueness 35S30: Fourier integral operators

Citation

Dan, Yuya. Uniqueness theorem in weighted Sobolev spaces of the Cauchy problem for Schrödinger type equations with variable coefficients. Adv. Differential Equations 13 (2008), no. 5-6, 489--507. https://projecteuclid.org/euclid.ade/1355867343.


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