Limiting Carleman weights and anisotropic inverse problems - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: In this article we consider the anisotropic Calderon problem and relatedinverse problems. The approach is based on limiting Carleman weights,introduced in Kenig-Sjoestrand-Uhlmann Ann. of Math. 2007 in the Euclideancase. We characterize those Riemannian manifolds which admit limiting Carlemanweights, and give a complex geometrical optics construction for a class of suchmanifolds. This is used to prove uniqueness results for anisotropic inverseproblems, via the attenuated geodesic X-ray transform. Earlier results indimension $n \geq 3$ were restricted to real-analytic metrics.



Author: D. Dos Santos Ferreira, C. E. Kenig, M. Salo, G. Uhlmann

Source: https://arxiv.org/







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