Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform

Authors
Greenleaf, A Uhlmann, G
Citation
A. Greenleaf et G. Uhlmann, Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform, DUKE MATH J, 108(3), 2001, pp. 599-617
Citations number
17
Categorie Soggetti
Mathematics
Journal title
DUKE MATHEMATICAL JOURNAL
ISSN journal
00127094 → ACNP
Volume
108
Issue
3
Year of publication
2001
Pages
599 - 617
Database
ISI
SICI code
0012-7094(20010615)108:3<599:LUFTDM>2.0.ZU;2-1
Abstract
We consider the Cauchy data associated to the Schrodinger equation with a p otential on a bounded domain Omega subset of R-n, n greater than or equal t o 3. We show that the integral of the potential over a two-plane Pi is dete rmined by the Cauchy data of certain exponentially growing solutions on any open subset U subset of partial derivative Omega which contains Pi boolean AND partial derivative Omega.