# Uniqueness for Inverse Boundary Value Problems by Cauchy Data on Subboundaries

Masahiro Yamamoto^{*}

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 subboundary to Neumann data on other subboundary. First we prove uniqueness results in three dimensions under some geometric conditions. Next we survey uniqueness results in two dimensions for various elliptic systems for arbitrarily given subboundary provided the input and the output subboundaries are the same. Our proof is based on complex geometric optics solutions which are constructed by a Carleman estimate.

Mathematics Subject Classification: 35R30 35R25

Keywords: inverse boundary value problems, uniqueness, Dirichlet-to-Neumann map, complex geometric optics solution

Minisymposion: Harmonic Analysis with Applications to Uniqueness and Inverse Estimates for PDEs