Limiting Carleman weights and anisotropic inverse problems

Details Limiting Carleman weights and anisotropic inverse problems Limiting Carleman weights and anisotropic inverse problems

2008-03-25

arxiv.org/abs/0803.3508v1

Mathematics

Analysis of PDEs

58 pages

Scientific paper

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 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 X-ray transform. Earlier results in dimension $n \geq 3$ were restricted to real-analytic metrics.

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