Year: 2007
Type: article
Abstract: In this paper we improve an earlier result by Bukhgeim and Uhlmann [1], by showing that in dimension n ≥ 3, the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential.We follow the general strategy of [1] but use a richer set of solutions to the Dirichlet problem.This implies a similar result for the problem of Electrical Impedance Tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary.Consequently the RHS of (7.12) tends to 0 as h → 0 and we get (5.18) as before, namely Ω q(x)a 2 (x)a 1 (x)e if (x) dx = 0. (7.13)Now the arguments of Section 6 imply that q = 0 finishing the proof of Theorem 1.1.
Source: Annals of Mathematics
Authors: Carlos Kenig, Gunther Uhlmann
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W2120896968