The Calderon problem with partial data

• 成果类型: Article
• 署名作者: Kenig, Carlos E.; Sjostrand, Johannes; Uhlmann, Gunther
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.165.567
• 发表日期: 2007
• 页码: 567-591
• 关键词: neumann map; uniqueness; equation

摘要

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 Schrodinger 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.