Global Uniqueness in Determining the Potential for the Two Dimensional Schrödinger Equation from Cauchy Data Measured on Disjoint Subsets of the Boundary

Abstract

We discuss the inverse boundary value problem of determining the potential in the two dimensional stationary Schrödinger equation from the pair of all Dirichlet data supported on an open subset Γ+ and all the corresponding Neumann data measured on an open subset Γ−. We prove global uniqueness, under some conditions, for the case that Γ+ and Γ− are disjoint. We construct appropriate complex geometrical optics solutions using Carleman estimates with a singular weight to prove the main result.

Cite this paper

@inproceedings{YuImanuvilov2011GlobalUI, title={Global Uniqueness in Determining the Potential for the Two Dimensional Schrödinger Equation from Cauchy Data Measured on Disjoint Subsets of the Boundary}, author={Oleg Yu.Imanuvilov and Gunther Uhlmann and Masahiro Yamamoto}, year={2011} }