Unique identifiability of the common support of coefficients of a second order anisotropic elliptic system by the Dirichlet–Neumann map

摘要

We consider the system of second order elliptic equations-∑k∇(Ei,k∇uk)+Pi,kuk=0,1⩽i⩽nin a bounded simply-connected domain B. Using a factorisation method ansatz, we show that the difference of two Neumann-to-Dirichlet maps Λ-Λ0 is sufficient to uniquely determine the support of the tensor E-E0 and the matrix P-P0, where E0 and P0 are known and-∑k∇(Ei,k0∇uk0)+Pi,k0uk0=0,1⩽i⩽n