Limiting Carleman weights and anisotropic inverse problems

• 成果类型: Article
• 署名作者: Ferreira, David Dos Santos; Kenig, Carlos E.; Salo, Mikko; Uhlmann, Gunther
• 署名单位: Universite Paris 13; University of Chicago; University of Helsinki; University of Washington; University of Washington Seattle
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0196-4
• 发表日期: 2009
• 页码: 119-171
• 关键词: boundary-value problem; conductivity problem; global uniqueness; 2 dimensions; neumann map; cauchy data; MANIFOLDS; equation; plane

摘要

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig et al. (Ann. Math. 165: 567-591, 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic ray transform. Earlier results in dimension n >= 3 were restricted to real-analytic metrics.