Let (Omega) over cap subset of R(2) be a bounded domain with a smooth boundary and (sigma) over cap s a smooth anisotropic conductivity on (Omega) over cap. Starting from the Dirichlet-to-Neumann operator Lambda((sigma) over cap) s on partial derivative(Omega) over cap, we give an explicit procedure to find a unique (up to a biholomorphism) domain Omega, an isotropic conductivity sigma on Omega and the boundary values of a quasiconformal diffeomorphism F : (Omega) over cap -> Omega which transforms (sigma) over cap into sigma.
On an inverse problem for anisotropic conductivity in the plane
Matteo Santacesaria
2010-01-01
Abstract
Let (Omega) over cap subset of R(2) be a bounded domain with a smooth boundary and (sigma) over cap s a smooth anisotropic conductivity on (Omega) over cap. Starting from the Dirichlet-to-Neumann operator Lambda((sigma) over cap) s on partial derivative(Omega) over cap, we give an explicit procedure to find a unique (up to a biholomorphism) domain Omega, an isotropic conductivity sigma on Omega and the boundary values of a quasiconformal diffeomorphism F : (Omega) over cap -> Omega which transforms (sigma) over cap into sigma.
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