THE Neumann problem for equations of Monge-Ampère type
THE Neumann problem for equations of Monge-Ampère type
复制标题
DOI：
10.1002/cpa.3160390405
复制
发表时间：
1986-07
影响因子：
3
通讯作者：
P. Lions;N. Trudinger;J. Urbas
中科院分区：
文献类型：
--
作者：
P. Lions;N. Trudinger;J. Urbas
证明了一类非线性Monge-Ampere型椭圆型方程Neumann型问题古典解的存在性。该方法依赖于建立一个先验导数估计高达二阶，并产生一个尖锐的结果，为规定的高斯曲率方程。我们还提出了应用程序的渐近问题，接近非唯一的情况下，最大值原则的线性方程的Aleksandrov-Bakelman型。
We prove the existence of a classical solution to a Neumann type problem for nonlinear elliptic equations of Monge-Ampere type. The methods depend upon the establishment of a priori derivative estimates up to order two and yield a sharp result for the equation of prescribed Gauss curvature. We also present applications to asymptotic problems which approach the non-unique case and maximum principles for linear equations of Aleksandrov-Bakelman type.