On Phragm\'en-Lindel\"of principle for Non-divergence Type Elliptic Equation and Mixed Boundary conditions

Paper 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 Phragm'en-Lindel"of theorem is proved at junction point of Dirichlet boundary and boundary over which derivative in non-tangential direction is defined.