On the decay of solutions of non-uniformly elliptic equations

We obtain upper and lower bounds for the rate of decay at infinity for a solution of a second-order non-uniformly elliptic equation in an unbounded domain with alternating types of boundary condition, both of the first and third types. We prove that the bound for this rate of decay is sharp, both in the case of a rather arbitrary alternation of boundary conditions of the first and third types and in the case of an equation degenerating on the boundary of an unbounded domain.