Classifying smooth supersolutions for a general class of elliptic boundary value problems

Abstract

This paper characterizes the pointwise behavior of smooth supersolutions of a general class of elliptic linear boundary value problems of mixed type. Our main result is a substantial extension of W.~Walter [9, Theorem 2] to cover the case of general mixed boundary conditions. As an application of this result, the theory of [6] is adapted to obtain a weak version---within the context of Schauder's theory---of the characterization of the strong maximum principle of H. Amann and J. López-Gómez [3].