A priori estimates for classical solutions of fully nonlinear elliptic equations

作者：Cao Yi^*; Li DongSheng; Wang LiHe

来源：Science China Mathematics, 2011, 54(3): 457-462.

DOI：10.1007/s11425-010-4092-6

• fully nonlinear
• classical solutions
• C-2,C-alpha estimates

For the fully nonlinear uniformly elliptic equation F(D (2) u) = 0, it is well known that the viscosity solutions are C (2,alpha) 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 C (1,beta) a.e. for any 0 < beta < 1. We will prove that the classical solutions u are C (2,alpha) . Moreover, the C (2,alpha) norm of u depends on n, F and the continuous modulus of D (2) u.

• 出版日期2011-3
• 单位西安交通大学