Related papers: Uniqueness in Calderon's problem with Lipschitz co…

We prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of two dimensional Maxwell's equations by partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…

Uniqueness in the Calder\'on problem in dimension bigger than two was usually studied under the assumption that conductivity has bounded gradient. For conductivities with unbounded gradients uniqueness results have not been known until…

It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex $n$-dimensional domain are uniformly Lipschitz. Applications of this result to some aspects of regularity of solutions to the Neumann problem…

We prove a global uniqueness result for the Calder\'{o}n inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension $n\ge 3$. Performing higher order linearizations of…

Let $M$ be a compact metric space and $X = M^{\mathbb{N}}$, we consider a set of admissible sequences $X_{A, I} \subset X$ determined by a continuous admissibility function $A : M \times M \to \mathbb{R}$ and a compact set $I \subset…

In two preceding articles, we studied the problem of the existence and uniqueness of a solution to some general BSDE on manifolds. In these two articles, we assumed some Lipschitz conditions on the drift $f(b,x,z)$. The purpose of this…

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…

For the linearized reconstruction problem in Electrical Impedance Tomography (EIT) with the Complete Electrode Model (CEM), Lechleiter and Rieder (2008 Inverse Problems 24 065009) have shown that a piecewise polynomial conductivity on a…

For Maxwell's equations in a wave guide, we prove the global uniqueness in determination of the conductivity, the permeability and the permittivity by partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

We show that Nachman's integral equations for the Calder\'on problem, derived for conductivities in $W^{2,p}(\Omega)$, still hold for $L^\infty$ conductivities which are $1$ in a neighborhood of the boundary. We also prove convergence of…

This work establishes a Lipschitz stability result for identifying unknown polygonal inclusions along with their unknown constant conductivity values, given boundary measurements encoded in the Dirichlet-to-Neumann map.

In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on $C^{1,1}$ domains. The first one is a sharp vanishing order estimate of Robin problems with Lipschitz coefficients…

We consider the Calder\'on problem for systems with unknown zeroth and first order terms, and improve on previously known results. More precisely, let $(M, g)$ be a compact Riemannian manifold with boundary, let $A$ be a connection matrix…

We consider Calder{\'o}n's problem on a class of Sobolev extension domains containing non-Lipschitz and fractal shapes. We generalize the notion of Poincar{\'e}-Steklov (Dirichlet-to-Neumann) operator for the conductivity problem on such…

We generalize many recent uniqueness results on the fractional Calder\'on problem to cover the cases of all domains with nonempty exterior. The highlight of our work is the characterization of uniqueness and nonuniqueness of partial data…

We address the stability issue in Calder\'on's problem for a special class of anisotropic conductivities of the form $\sigma=\gamma A$ in a Lipschitz domain $\Omega\subset\mathbb{R}^n$, $n\geq 3$, where $A$ is a known Lipschitz continuous…

This paper is devoted to the reconstruction of the time and space-dependent coefficient in an infinite cylindrical hyperbolic domain. Using a local Carleman estimate we prove the uniqueness and a H\"older stability in the determining of the…

We prove uniqueness of the inverse conductivity problem in three dimensions for complex conductivities in $W^{1,\infty}$. We apply quaternionic analysis to transform the inverse problem into an inverse Dirac scattering problem, as…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…