Abstract
Abstract
For the Lamé operator
with variable coefficients λ and µ on a smooth compact Riemannian manifold (M, g) with smooth boundary
∂
M
, we give an explicit expression for the full symbol of the elastic Dirichlet-to-Neumann map
Λ
λ
,
μ
. We show that
Λ
λ
,
μ
uniquely determines the partial derivatives of all orders of the Lamé coefficients λ and µ on
∂
M
. Moreover, for a nonempty smooth open subset
Γ
⊂
∂
M
, suppose that the manifold and the Lamé coefficients are real analytic up to Γ, we prove that
Λ
λ
,
μ
uniquely determines the Lamé coefficients on the whole manifold
M
ˉ
.
Funder
National Natural Science Foundation of China
National Key Research and Development Program of China
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science