Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform
Abstract
We consider the Dirichlet-to-Neumann 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 two-plane is determined by the Cauchy data of certain exponentially growing solutions on any neighborhood of the intersection of the two-plane with the boundary.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 2000
- DOI:
- 10.48550/arXiv.math/0001099
- arXiv:
- arXiv:math/0001099
- Bibcode:
- 2000math......1099G
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- Mathematics - Mathematical Physics;
- 35R30;
- 44A12
- E-Print:
- Final revision, to appear in the Duke Mathmematical Journal