Limiting Carleman weights and anisotropic inverse problems
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In this article, the authors considered the anisotropic Calderon problem and related inverse problems, and characterized those Riemannian manifolds which admit limiting Carleman weights, and gave a complex geometrical optics construction for a class of such manifolds.Abstract:
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.read more
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The Poisson embedding approach to the Calder\'on problem
TL;DR: In this paper, a map called Poisson embedding is introduced to identify the points of a Riemannian manifold with distributions on its boundary, leading to a new uniqueness result for a large class of Calderon type inverse problems for quasilinear equations in the real analytic case.
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Broken ray transform on a Riemann surface with a convex obstacle
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TL;DR: In this paper, the authors considered the broken ray transform on Riemann surfaces in the presence of an obstacle and showed that a function is determined by its integrals over broken geodesic rays that reflect on the boundary of the obstacle.
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On non-uniqueness for the anisotropic Calderón problem with partial data
TL;DR: In this paper, the Calderon problem with partial data for Riemannian metrics with Holder continuous coefficients in dimension greater or equal than three was shown to be non-uniqueness.
References
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The Analysis of Linear Partial Differential Operators I
TL;DR: In this article, the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certain products using instruction manuals, which are clearlybuilt to give step-by-step information about how you ought to go ahead in operating certain equipments.
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A global uniqueness theorem for an inverse boundary value problem
John Sylvester,Gunther Uhlmann +1 more
TL;DR: In this paper, the single smooth coefficient of the elliptic operator LY = v yv can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed region 2 C R', n? 3.
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