On the strong maximum principle.

In this paper we study the strong maximum principle for equations of the form F [ u ] = H (u , | D u |) where F is either a fully nonlinear elliptic operator or is the p-Laplace operator. We give sufficient conditions on H to ensure that the strong maximum principle (SMP) holds. The condition is also necessary for SMP to hold for the the equation F [ u ] = g (| D u |). [ABSTRACT FROM AUTHOR]