上半凹函数和下半凸函数的一阶粘性导数的存在性

Existence of Viscosity Derivatives for the Super Concave Functions and Sub Convex Functions

首先弱化了常规的凹函数和凸函数的概念,给出了几乎处处可微函数的上半凹函数和下半凸函数的概念,在此基础上用非光滑分析得出了上半凹函数和下半凸函数的一阶粘性上(下)导数的存在性.

By giving definitions of the super concave functions and sub convex functions,the existence of viscosity derivatives of the super concave functions and sub convex functions are discussed.