Limiting Carleman weights and anisotropic inverse problems
Reads0
Chats0
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
More filters
Journal ArticleDOI
Tensor tomography: Progress and challenges
TL;DR: In this paper, the authors survey recent progress in the problem of recovering a tensor field from its integrals along geodesics and propose several open problems, such as recovering tensor fields from their integrals.
Journal ArticleDOI
Carleman estimates and inverse problems for Dirac operators
Mikko Salo,Leo Tzou +1 more
TL;DR: In this paper, the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator was considered, and it was shown that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators.
Journal ArticleDOI
Calderon inverse Problem with partial data on Riemann Surfaces
Colin Guillarmou,Leo Tzou +1 more
TL;DR: In this article, it was shown that the Dirichlet-to-Neumann map on a fixed smooth compact Riemann surface with boundary (M_0,g) determines uniquely the potential of the Schrodinger operator.
Journal ArticleDOI
Calderón inverse problem with partial data on Riemann surfaces
Colin Guillarmou,Leo Tzou +1 more
TL;DR: For the Schrodinger operator Δg+V with potential V ∈ C1,α(M0) for some α>0, the Dirichlet-to-Neumann map N|Γ measured on an open set Γ⊂∂M0 determines uniquely the potential V as discussed by the authors.
Journal ArticleDOI
The Calderón problem for variable coefficients nonlocal elliptic operators
TL;DR: In this paper, the inverse problem of a Schrodinger type variable nonlocal elliptic operator (−∇⋅(A(x)∇))s+q for any dimension n ≥ 2 was introduced.
References
More filters
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.
Related Papers (5)
A global uniqueness theorem for an inverse boundary value problem
John Sylvester,Gunther Uhlmann +1 more
Determining anisotropic real-analytic conductivities by boundary measurements
John M. Lee,Gunther Uhlmann +1 more