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 $\nabla \cdot \vec{C}(x,\nabla u(x))=0$, in a bounded smooth domain $\Omega$. We assume that $\overrightarrow{C}(x,\vec{p})=\gamma (x)\vec{p}+\vec{b}(x)|\vec{p}{|}^2+\mathcal{O}(|\vec{p}{|}^3)$, by expanding $\overrightarrow{C}(x,\vec{p})$ around $\vec{p}=0$. We give a reconstruction method for $\gamma$ and $\vec{b}$ from the Dirichlet to Neumann map defined on $\partial \Omega$.

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