For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutio...For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10771166)
文摘For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u.
