$W^{4, p}$ solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations
$W^{4, p}$ solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations
复制标题
DOI：
10.1016/j.jde.2015.11.013
复制
发表时间：
2015-06
期刊：
影响因子：
--
通讯作者：
N. Le
中科院分区：
文献类型：
--
作者：
N. Le
仿射平均曲率方程的第二边值问题是一个非线性的四阶几何偏微分方程。它是由Trudinger和Wang在2005年在他们对仿射几何中的仿射高原问题的研究中引入的。Trudinger-Wang，Chau-Weinkove和作者以前的工作在对仿射平均曲率的符号或可积性的某些限制下解决了W4，p中的这个整体问题。当仿射平均曲率属于Lp且p大于维数时，本文去掉了这些限制，得到了第二边值问题的W4，p解.我们的独立分析也涵盖了Abreu方程的情况。
The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger–Wang, Chau–Weinkove and the author solved this global problem in W 4, p under some restrictions on the sign or integrability of the affine mean curvature. We remove these restrictions in this paper and obtain W 4, p solution to the second boundary value problem when the affine mean curvature belongs to L p with p greater than the dimension. Our self-contained analysis also covers the case of Abreu's equation.