ﻻ يوجد ملخص باللغة العربية
In this article we study the linearized anisotropic Calderon problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderon problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the transversal manifold, with exponentially small errors, as well as the FBI transform characterization of the analytic wave front set.
We show that a continuous potential $q$ can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the Schrodinger operator $-Delta_g+q$ on a conformally transversally anisotropic manifold of dimension $geq 3$, provided t
Uniqueness and reconstruction in the three-dimensional Calderon inverse conductivity problem can be reduced to the study of the inverse boundary problem for Schrodinger operators $-Delta +q $. We study the Born approximation of $q$ in the ball, which
We consider the so called Calderon problem which corresponds to the determination of a conductivity appearing in an elliptic equation from boundary measurements. Using several known results we propose a simplified and self contained proof of this result.
We consider the inverse Calderon problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually assumes the
In these notes we prove log-type stability for the Calderon problem with conductivities in $ C^{1,varepsilon}(bar{Omega}) $. We follow the lines of a recent work by Haberman and Tataru in which they prove uniqueness for $ C^1(bar{Omega}) $.