We study the general equation b(u)−a(u,φ(u)x)x=f of second order elliptic type, which may degenerate onto a first order equation for some value of u. We introduce for that a notion of entropy type solution for the elliptic problem. We define an L1 operator associated to the equation. We show that the operator is accretive in L1, with dense domain and verify the range condition.

elliptic equation; weak solution; entropy solution; accretive operator