Hopf's lemma for a class of singular/degenerate PDE-s

Abstract

This paper concerns Hopf's boundary point lemma, in certain C 1,Dini -type domains, for a class of singular/degenerate PDE-s, including p-Laplacian. Using geometric properties of levels sets for harmonic functions in convex rings, we construct sub-solutions to our equations that play the role of a barrier from below. By comparison principle we then conclude Hopf's lemma.