The linearized Calderon problem in transversally anisotropic geometries

Abstract

In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an FBI type transform at certain points in the transversal manifold. This leads to recovery of transversal singularities in the linearized problem. The method requires a geometric condition on the transversal manifold related to pairs of intersecting geodesics, but it does not involve the geodesic X-ray transform which has limited earlier results on this problem.

arXiv comment27 pages

References in corpus (3)

• Limiting Carleman weights and anisotropic inverse problems
• Calderon inverse Problem with partial data on Riemann Surfaces
• Local analytic regularity in the linearized Calderón problem

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• Inverse problems for non-linear hyperbolic equations with disjoint sources and receivers
• Stability estimates for inverse problems for semi-linear wave equations on Lorentzian manifolds