On the inverse conductivity problem

摘要

It is shown here that for the boundary value problem div(a∇u)=δ(x∗)inRn,u(x)→0as|x|→∞ in order to identify the coefficient a, one needs on additional data u(x,x∗)=g(x,x∗), where x∈Γ1,x∗∈Γ2,Γ1,Γ2 are two open nonempty subsurfaces of ∂Ω (Ω is a domain with analytic boundary which contains a bounded set V) and a∈H2,pp⩾n/2 and a satisfies conditions of Lemma 2. Here we also prove that the uniqueness of a entering to the problem the additional data.