Some properties of solutions of degenerate second order P.D.E. in non-divergence form

Abstract

In this paper we study some properties of solution of F(x,u,D²u)=f. The appearance of a null set is derived from an assumption of degeneracy at the origin, involving the dependence of F on the zeroth and second derivative terms. The non appearance of a null set is obtained by the strong maximum principle of Hopf when a strong non degeneracy assumption holds. Interior properties of solutions of F(x,u,D²u)=f on R^N are also obtained under another assumption of degeneracy at infinity.

AMS(OMS):

• 35B05
• 35B50
• 35R35