Before revision: We prove weak and strong maximum principles, including a Hopf lemma, for classical solutions to equations defined by linear, second-order, partial differential operators with non-negative characteristic form (degenerate-elliptic operators), in the presence of a second-order boundarycondition of Ventcel type along the degeneracy locus of the principle symbol of the operator on the domain boundary.
After revision: We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators with non-negative characteristic form (degenerate-elliptic operators), in the presence of a second-order boundarycondition of Ventcel type along the degeneracy locus of the principle symbol of the operator on the domain boundary.