Behaviour at infinity for solutions of a mixed nonlinear elliptic boundary value problem via inversion

We study a mixed boundary value problem for the quasilinear elliptic equation div A(x, del u(x)) = 0 in an open infinite circular half-cylinder with prescribed continuous Dirichlet data on a part of the boundary and zero conormal derivative on the rest. The equation is assumed to satisfy the standard ellipticity conditions with a parameter p > 1. We prove the existence and uniqueness of bounded weak solutions to the mixed problem and characterize the regularity of the point at infinity in terms of p-capacities. For solutions with only Neumann data near the point at infinity we show that they behave in exactly one of three possible ways, similar to the alternatives in the Phragmen-Lindelof principle.