Stability of the Inverse Conductivity Problem in the Plane for Less Regular Conductivities

The Dirichlet to Neumann map Λγ, or voltage to current map, takes Dirichlet data u=f ∂Ω to the conormal derivatives γ 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+ (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