On the Hopf–Oleinik lemma for degenerate-elliptic equations at characteristic points

In this paper we discuss the validity of the Hopf lemma at boundary points which are characteristic with respect to certain degenerate-elliptic equations. In the literature there are some positive results under the assumption that the boundary of the domain reflects the underlying geometry of the specific operator. We focus here on conditions on the boundary which are suitable for some families of degenerate operators, also in presence of first order terms.