Reconstruction for the coefficients of a quasilinear elliptic partial differential equation

Abstract

In this paper we consider an inverse coefficients problem for a quasilinear elliptic equation of divergence form ∇⋅C→(x,∇u(x))=0, in a bounded smooth domain Ω. We assume that C⃗(x,p→)=γ(x)p→+b→(x)|p→|2+O(|p→|3), by expanding C⃗(x,p→) around p→=0. We give a reconstruction method for γ and b→ from the Dirichlet to Neumann map defined on ∂Ω.