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

Abstract

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