Local uniqueness for the DirichlettoNeumann map via the twoplane transform
Abstract
We consider the DirichlettoNeumann map associated to the Schrödinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potential over a twoplane is determined by the Cauchy data of certain exponentially growing solutions on any neighborhood of the intersection of the twoplane with the boundary.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2000
 arXiv:
 arXiv:math/0001099
 Bibcode:
 2000math......1099G
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 35R30;
 44A12
 EPrint:
 Final revision, to appear in the Duke Mathmematical Journal