On Hopf's Lemma and the Strong Maximum Principle
  In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle. 
S. Bertone, A. Cellina, E. M. Marchini