Generalized Maximum Principle for Divergence Form Elliptic Equations in Unbounded Domains

In this note I extend some previuos results concerning a generalized maximum principle for linear second order elliptic equations in divergence form, to the case of unbounded domains. In this situation the complete continuity of the immersion of H^1(Omega) in L^2(Omega) is no longer true, so that many of the proofs already used must be completely changed.