RECONSTRUCTION OF LESS REGULAR CONDUCTIVITIES IN THE PLANE

KIM KNUDSEN ALEXANDRU TAMASAN

Abstract. We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution γ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction algorithm for the conductivity γ ∈ C^{1+ϵ}(\overline{Ω}) in the plane domain Ω from the associated Dirichlet to Neumann map on ∂Ω. Hence we improve earlier reconstruction results. The method used relies on a well-known reduction to a first order system, for which the \overline{∂}-method of inverse scattering theory can be applied.