Inverse Problems for Scalar Elliptic Equations and Systems

Abstract

In this thesis, we discuss inverse boundary value problems for scalar equations and for systems. First we introduce the famous Calder\'on problem and its recent developments. We focus on deriving the stability estimate of the conductivities from the partial Cauchy data. Second, we consider inverse boundary value problems for Stokes and Navier--Stokes equations and demonstrate the global uniqueness for viscosity in dimension two.