Differential and Integral Equations

Uniqueness theorem of the Cauchy problem for Schrödinger's equation in weighted Sobolev spaces

Yuya Dan

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Abstract

The present paper is concerned with the uniqueness of solutions to the Cauchy problem for the free Schrödinger equation. It is proved by the wellposedness of the associated adjoint problem that the solution to the Cauchy problem is unique in exponential weighted Sobolev spaces.

Article information

Source
Differential Integral Equations, Volume 18, Number 11 (2005), 1257-1271.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356059741

Mathematical Reviews number (MathSciNet)
MR2174820

Zentralblatt MATH identifier
1212.35378

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35S30: Fourier integral operators

Citation

Dan, Yuya. Uniqueness theorem of the Cauchy problem for Schrödinger's equation in weighted Sobolev spaces. Differential Integral Equations 18 (2005), no. 11, 1257--1271. https://projecteuclid.org/euclid.die/1356059741


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