Stability of the inverse conductivity problem in the plane for less regular conductivities

Abstract

The Dirichlet to Neumann map Λγ, or voltage to current map, takes Dirichlet data u=f∈∂Ω to the conormal derivatives γ∂u∂η at the boundary ∂Ω, where u is a solution to the elliptic equation div(γ∇u)=0. On a plane Lipchitz domain Ω⊂R2, we consider the inverse conductivity problem that consists of the recovery of γ in the interior of Ω from the knowledge of Λγ. We prove stability for this inverse map, assuming an isotropic conductivity γ∈C1+ε(Ω). We reduce the equation div(γ∇u)=0 to an equivalent system and use the ∂∂-scattering transform. This approach relaxes the number of derivatives of γ required in former works. © 2001 Academic Press.