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

TL;DR

This paper investigates the Phragmén-Lindelöf principle for non-divergence elliptic equations with mixed boundary conditions, establishing a growth lemma and a boundary theorem in Lipschitz domains.

Contribution

It introduces a Landis-type growth lemma and proves a Phragmén-Lindelöf theorem for mixed boundary value problems in admissible Lipschitz domains.

Findings

Established a Landis-type growth lemma in spherical layers.

Proved a Phragmén-Lindelöf theorem at boundary junction points.

Extended principles to non-divergence elliptic equations with mixed boundary conditions.

Abstract

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.