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 $\gamma$ is a complex valued $L^\infty$ coefficient, satisfying a strong ellipticity condition. In Electrical Impedance Tomography, $\gamma$ represents the admittance of a conducting body. An interesting issue is the one of determining $\gamma$ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map $\Lambda_\gamma$. Under the above general assumptions this problem is an open issue. In this paper we prove that, if we assume a priori that $\gamma$ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of $\gamma$ from $\Lambda_\gamma$ 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 $\lambda$, $\mu$ 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 $\lambda$ and $\mu$ 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