完全非线性单调二阶椭圆方程组Neumann问题上解和下解的存在性

The Existence of the Supersolution and Subsolution of the Neumann Problems of the Fully Nonlinear Monotone Second-order Elliptic Systems

HitoshiIshii和ShigeakiKoike在[1]中讨论了完全非线性单调二阶椭圆方程的粘性解的存在唯一性。本文通过改进单调性结构条件,将有些结论推广到完全非线性单调二阶椭圆方程组Neumann问题上去。首先给出了完全非线性单调二阶椭圆方程组Neumann问题上解和下解的定义,然后证明了这类方程组Neumann问题上解和下解的存在性。

In [ 1 ], Hitoshi Ishii and Shigeaki Koike discuss the existence and uniqueness for the viscosity solutions of the fully nonlinear monotone second-order elliptic equations. In this paper, we extend case some their conclusions to systems and prove the existence for supersolution and subsolution in systems.