Limiting Carleman weights and anisotropic inverse problems
TLDR
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
Citations
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Rigidity of inverse problems for nonlinear elliptic equations on manifolds
TL;DR: In this paper , the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map is considered.
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Reconstruction in the Calder\'on problem on conformally transversally anisotropic manifolds
TL;DR: In this article, it was shown that a continuous potential can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the Schrodinger operator on a conformally transversally anisotropic manifold, provided that the geodesic ray transform on the transversal manifold is constructively invertible.
References
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BookDOI
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.
Book
Riemannian geometry and geometric analysis
TL;DR: A very readable introduction to Riemannian geometry and geometric analysis can be found in this paper, where the author focuses on using analytic methods in the study of some fundamental theorems in Riemmannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, Lyusternik and Fet theorem and the existence of harmonic mappings.
Journal ArticleDOI
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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