164 research outputs found
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
Uniqueness and Lipschitz stability for the identification of Lam\'e parameters from boundary measurements
In this paper we consider the problem of determining an unknown pair
, of piecewise constant Lam\'{e} parameters inside a three
dimensional body from the Dirichlet to Neumann map. We prove uniqueness and
Lipschitz continuous dependence of and from the Dirichlet to
Neumann map
A transmission problem on a polygonal partition: regularity and shape differentiability
We consider a transmission problem on a polygonal partition for the
two-dimensional conductivity equation. For suitable classes of partitions we
establish the exact behaviour of the gradient of solutions in a neighbourhood
of the vertexes of the partition. This allows to prove shape differentiability
of solutions and to establish an explicit formula for the shape derivative
An asymptotic formula for the displacement field in the presence of thin elastic inhomogeneities
We consider a plane isotropic homogeneous elastic body with thin elastic inhomogeneities in the form of small neighborhoods of simple smooth curves. We derive a rigorous asymptotic expansion of the boundary displacement field as the thickness of the neighborhoods goes to zero. © 2006 Society for Industrial and Applied Mathematics
Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation
We study an inverse boundary value problem for the Helmholtz equation using
the Dirichlet-to-Neumann map as the data. We consider piecewise constant
wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability
estimate in terms of the Hausdorff distance between partitions
Size estimates for the EIT problem with one measurement: the complex case
In this paper we estimate the size of a measurable inclusion in terms of
power measurements for a single applied boundary current. This problem arises
in medical imaging for the screening of organs. For this kind of problem one
has to deal mathematically with the complex conductivity (admittivity)
equation. In this case we are able to establish, for certain classes of
admittivities, lower and upper bounds of the measure of the inclusion in terms
of the power measurements. A novelty of our result is that we are able to
estimate also the volume of inclusions having part of its boundary in common
with the reference body. Our analysis is based on the derivation of energy
bounds and of fine quantitative estimates of unique continuation for solutions
to elliptic equations
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