On the Maximum Principle for Solutions of Second Order Elliptic Equations

In this paper, we found sufficient conditions, under fulfillment of which the maximum principle for the solution of a second order partial differential elliptic equation in the unit circle meets maximum principle. It is proved that if a quasiconformality coefficient of such function satisfies certain boundary conditions, then this function meets maximum principle. While proving the main result, we use integral representations of solutions of this equation and properties of the Cauchy type integral and functions of Hardy and Smirnoff classes.