238 research outputs found
Uniqueness in the Inverse Conductivity Problem for Complex-Valued Lipschitz Conductivities in the Plane
We consider the inverse impedance tomography problem in the plane. Using Bukhgeim's scattering data for the Dirac problem, we prove that the conductivity is uniquely determined by the Dirichlet-to-Neuman map.
Read More: http://epubs.siam.org/doi/abs/10.1137/17M112098
Uniqueness in Calderon's problem with Lipschitz conductivities
We use X^{s,b}-inspired spaces to prove a uniqueness result for Calderon's
problem in a Lipschitz domain under the assumption that the conductivity is
Lipschitz. For Lipschitz conductivities, we obtain uniqueness for
conductivities close to the identity in a suitable sense. We also prove
uniqueness for arbitrary C^1 conductivities.Comment: 14 page
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 when the so-called
Neumann-to-Dirichlet map is locally given on a non empty curved portion
of the boundary . We prove that anisotropic
conductivities that are \textit{a-priori} known to be piecewise constant
matrices on a given partition of with curved interfaces can be
uniquely determined in the interior from the knowledge of the local
Neumann-to-Dirichlet map
Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities
We consider the electrostatic inverse boundary value problem also known as
electrical impedance tomography (EIT) for the case where the conductivity is a
piecewise linear function on a domain and we show
that a Lipschitz stability estimate for the conductivity in terms of the local
Dirichlet-to-Neumann map holds true.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1405.047
Lipschitz stability for the electrical impedance tomography problem: the complex case
In this paper we investigate the boundary value problem {div(\gamma\nabla
u)=0 in \Omega, u=f on \partial\Omega where is a complex valued
coefficient, satisfying a strong ellipticity condition. In
Electrical Impedance Tomography, represents the admittance of a
conducting body. An interesting issue is the one of determining
uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map
. Under the above general assumptions this problem is an open
issue.
In this paper we prove that, if we assume a priori that is piecewise
constant with a bounded known number of unknown values, then Lipschitz
continuity of from holds
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