Uniqueness in Calderón’s Problem for Conductivities with Unbounded Gradient

Global Uniqueness for the Calderón Problem with Lipschitz Conductivities

We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the threeand four-dimensional cases, this confirms a conjecture of Uhlmann. Our proof builds on the work of Sylvester and Uhlmann, Brown, and Haberman and Tataru who proved uniqueness for C1-conductivities and Lipschitz conductivities sufficient...

Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω ⊂ Rn when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion Σ of the boundary ∂Ω. We prove that anisotropic conductivities that are a-priori known to be piecewise constant matrices on a given partition of Ω with curved interfaces can be uniquely determined in the...

Uniqueness in the Inverse Conductivity Problem for Nonsmooth Conductivities in Two Dimensions

Let R 2 be a bounded domain with Lipschitz boundary and let : ! R be a function which is measurable and bounded away from zero and innnity. We consider the divergence form elliptic operator

Global Uniqueness in the Impedance Imaging Problem for Less Regular Conductivities

If L = divr is an elliptic operator with scalar coeecient , we show that we can recover the coeecient from the Dirichlet to Neumann map under the assumption that has only 3=2 + derivatives. Previously, the best result required to have two derivatives. Let R n ; n 3, be a bounded open set and let L = div r be an elliptic operator on with scalar coeecient. We let denote the Dirichlet to Neumann m...

Uniqueness Theorems for Multidimensional inverse Problems with Unbounded Coefficients