Detecting Anisotropic Inclusions Through EIT

We study the evolution equation ∂_tu=-Λ_tu where Λ_t is the Dirichlet–Neumann operator of a decreasing family of Riemannian manifolds with boundary Σ_t . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the restriction of harmonic functions on ℳ=Σ_0 to the boundaries of ∂Σ_t . Consequently we are able to derive a lower bound for the difference of the Dirichlet–Neumann maps in terms of the difference of a background metrics g and an inclusion metric g+χ_Σ(h-g) on a manifold ℳ .