Inverse boundary value problems with partial data in unbounded domains

Abstract

We study the inverse boundary value problems for matrix-valued Schrödinger equations in two types of unbounded domains—infinite slab and half-space. We prove that the coefficients can be determined uniquely up to a gauge equivalent class from partial measurements about the solutions on the boundary. The boundary measurements are known only on the same single hyperplane of the slab or on (the same) part of the boundary of the half-space. The study of inverse problems for the matrix-valued Schrödinger equations will be a prototype in the study of inverse problems for systems of differential equations. An infinite slab and a half-space are important geometries in applications, such as seismic prospecting, medical imaging and wave guide.