Mixed boundary value problems for non-divergence type elliptic equations in unbounded domains

We investigate the qualitative properties of solution to the Zaremba type problem in unbounded domain for the non-divergence elliptic equation with possible degeneration at infinity. The main result is Phragmén-Lindelöf type principle on growth/decay of a solution at infinity depending on both the structure of the Neumann portion of the boundary and the ”thickness” of its Dirichlet portion. The result is formulated in terms of so-called s-capacity of the Dirichlet portion of the boundary, while the Neumann boundary should satisfy certain “admissibility” condition in the sequence of layers converging to infinity.

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