Related papers: Uniqueness in Calderon's problem with Lipschitz co…
We prove uniqueness for Calder\'on's problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and four dimensional cases, this confirms a conjecture of Uhlmann. Our proof…
We prove uniqueness in the inverse conductivity problem for uniformly elliptic conductivities in $W^{s,p}(\Omega)$, where $\Omega \subset \mathbb R^n$ is Lipschitz, $3\leq n \leq 6$, and $s$ and $p$ are such that $ W^{s,p}(\Omega)\not…
The Calder\'on problem is an inverse problem with applications to electrical impedance tomography and geophysical prospection. We prove uniqueness in the Calder\'on problem in spatial dimension $n \geq 3$ for scalar conductivities in the…
In this note, we study Calder\'on's problem for certain classes of conductivities in domains with circular symmetry in two and three dimensions. Explicit formulas are obtained for the reconstruction of the conductivity from the…
We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz…
In dimensions greater than or equal to three, we establish global uniqueness and obtain reconstruction in the Calderon problem for the Schrodinger equation with certain singular potentials. The potentials considered are conormal of order…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
Calder\'on's inverse conductivity problem has, so far, only been subject to conditional logarithmic stability for infinite-dimensional classes of conductivities and to Lipschitz stability when restricted to finite-dimensional classes.…
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…
We prove that an $L^\infty$ potential in the Schr\"odinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a known finite dimensional subspace…
Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the conductivity is indeed…
It is proved that, in two dimensions, the Calder\'on inverse conductivity problem in Lipschitz domains is stable in the $L^p$ sense when the conductivities are uniformly bounded in any fractional Sobolev space $W^{\alpha,p}$ $\alpha>0,…
We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.
We consider the so called Calder\'on 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…
In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain $\Omega\subset\RR^n$, with $L^\infty$ Robin coefficient, $L^2$ Neumann data and isotropic conductivity of class $W^{1,r}(\Omega)$,…
We consider one-dimensional Calder\'on's problem for the variable exponent $p(\cdot)$-Laplace equation and find out that more can be seen than in the constant exponent case. The problem is to recover an unknown weight (conductivity) in the…
In this paper we study the inverse conductivity problem with partial data. Moreover, we show that, in dimension $n\geq 3$ the uniqueness of the Calder\'{o}n problem holds for the $C^{1}\bigcap H^{3/2, 2}$ conductivities.
In this paper we show uniqueness of the conductivity for the quasilinear Calder\'on's inverse problem. The nonlinear conductivity depends, in a nonlinear fashion, of the potential itself and its gradient. Under some structural assumptions…
We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…
The unique determination of a measurable conductivity from the Dirichlet-to-Neumann map of the equation $\mathrm{div} (\sigma \nabla u) = 0$ is the subject of this note. A new strategy, based on Clifford algebras and a higher dimensional…