Journal of innovative applied mathematics and computational sciences
Volume 1, Numéro 1, Pages 48-63
2021-12-30
Recent Progress In The Conductivity Reconstruction In Calderón’s Problem
Authors : Aoudj Manal .
Abstract
In this work, we study a nonlinear inverse problem for an elliptic partial differential equation known as the Calderón problem or the inverse conductivity problem. We give a short survey on the reconstruction question of conductivity from measurements on the boundary by covering the main currently known results regarding the isotropic problem with full data in two and higher dimensions. We present Nachman’s reconstruction procedure and summarize the theoretical progress of the technique to more recent results in the field. An open problem of significant interest is proposed to check whether it is possible to extend the method for Lipschitz conductivities.
Keywords
Boundary integral equation, Calderón problem Inverse conductivity problem , Dirichlet-to-Neumann map, Complex geometrical optics solutions
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