LOCAL STABILITY IN A MINIMIZATION PROBLEM FOR CONDUCTIVITY IMAGING

Abstract. We consider the problem of minimization of the func-tional Ω a(x)|∇u(x)|dx over functions u of bounded variation with prescribed trace f at the boundary. The stability of the minimum value of the functional with respect to the coefficient a ∈ L2(Ω) is established in the vicinity of a coefficient of the form a = σ|∇u|, where u solves ∇ · σ∇u = 0 with u|∂Ω = f. This problem occurs in conductivity imaging when knowledge of the magnitude of the current density field inside a body is available. The method of proof is constructive