Uniqueness for inverse boundary value problems by Dirichlet-to -Neumann map on subboundaries

Abstract

We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial \Omega \setminus {\Gamma }_{-}$ to Neumann data on $\partial \Omega \setminus {\Gamma }_{+}$. First we prove uniqueness results in three dimensions under some conditions such as $\overline{{\Gamma }_{+}\cup {\Gamma }_{-}}=\partial \Omega$. Next we survey uniqueness results in two dimensions for various elliptic systems for arbitrarily given ${\Gamma }_{-}={\Gamma }_{+}$. Our proof is based on complex geometric optics solutions which are constructed by a Carleman estimate.

References in corpus (2)

• Inverse Boundary Value Problem by Partial data for the Neumann-to-Dirichlet-map in two dimensions
• Inverse boundary value problem for linear Schrödinger equation in two dimensions