论文标题
最大原则和移动飞机的方法
Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications
论文作者
论文摘要
在本文中，我们建立了各种最大原则，并开发了移动平面的方法和涉及统一椭圆形非本地贝尔曼操作员的方程式的滑动方法（在一般无界域上）。结果，我们得出了这些最大原则和移动平面方法的多个应用。例如，我们证明了对涉及有限域，无界域，ePigraph或$ \ mathbb {r}^{n} $的各种方程的解决方案的对称性，单调性和唯一性结果和渐近性。特别是，Caffarelli和Charro在\ cite {cc}中引入的均匀的椭圆形非本地蒙格 - 安培操作员是统一的椭圆形非局部贝尔曼操作员的典型例子。
In this paper, we establish various maximum principles and develop the method of moving planes and the sliding method (on general unbounded domains) for equations involving the uniformly elliptic nonlocal Bellman operator. As a consequence, we derive multiple applications of these maximum principles and the moving planes method. For instance, we prove symmetry, monotonicity and uniqueness results and asymptotic properties for solutions to various equations involving the uniformly elliptic nonlocal Bellman operator in bounded domains, unbounded domains, epigraph or $\mathbb{R}^{n}$. In particular, the uniformly elliptic nonlocal Monge-Ampère operator introduced by Caffarelli and Charro in \cite{CC} is a typical example of the uniformly elliptic nonlocal Bellman operator.
