Propagation of Smallness and the Uniqueness of Solutions to Some Elliptic Equations in the Plane

In this paper we prove theorems on propagation of smallness and the uniqueness of solutions to some elliptic equations in the plane. We start with analogues of these theorems for harmonic functions and use their quasiinvariance under quasiconformal mappings as well as the connection of considered equations with such mappings.