On Phragmén — Lindelöf principle for Non-divergence Type Elliptic Equations and Mixed Boundary conditions

The paper is dedicated to qualitative study of the solution of the Zaremba-type problem in Lipschitz domain with respect to the elliptic equation in non-divergent form. Main result is Landis type Growth Lemma in spherical layer for Mixed Boundary Value Problem in the class of “admissible domain”. Based on the Growth Lemma Phragmén — Lindelöf theorem is proved at junction point of Dirichlet boundary and boundary over which derivative in non-tangential direction is defined.