We consider the conductivity problem in two dimensions. We show that a complexvalued coefficient γ , whose imaginary part is small, can be recovered from the knowledge of the Dirichlet-to-Neumann map.
We consider a conducting body with complex valued admittivity containing a finite number of well separated thin inclusions. We derive an asymptotic formula for the boundary values of the potential in terms of the width of the inclusions.
In this paper we investigate the boundary value problemwhere γ is a complex valued L ∞ coefficient, satisfying a strong ellipticity condition. In Electrical Impedance Tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map Λγ . Under the above general assumptions this problem is an open issue.In this paper we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from Λγ holds.
We treat the stability issue for the three dimensional inverse imaging modality called Quantitative Photoacoustic Tomography. We provide universal choices of the illuminations which enable to recover, in a Hölder stable fashion, the diffusion and absorption coefficients from the interior pressure data. With such choices of illuminations we do not need the nondegeneracy conditions commonly used in previous studies, which are difficult to be verified a-priori.
Abstract. We consider the inverse problem of determining the Lamé parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse problem when the Lamé parameters and the density are assumed to be piecewise constant on a given domain partition.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.