Hessian型方程Neumann边值问题的梯度估计
The Gradient Estimates of Hessian Type Equations for Neumann Boundary Value Problem

通过构造辅助函数, 利用基本对称函数的性质以及函数在极大值点的性质, 得到Hessian型方程$S_{k}(D^{2}u-A(x,u,Du))=B(x,u)$的梯度内估计, 构造不同的辅助函数, 分近边、边界和内部3种情形讨论该方程Neumann边值问题, 进而得到全局梯度估计.
In the paper, according to the property of elementary symmetric function and the property of the maximum value point, gradient inner estimates of Hessian type equations $S_{k}(D^{2}u-A(x,u,Du))=B(x,u)$ are obtained by the method of auxiliary functions. Then, by constructing different auxiliary functions, the authors study the global gradient estimates of the Hessian type equations for Neumann boundary value problem for three different situations: Boundary, near the boundary and inner.