论文标题
统一的$ n $ -th订单式泳道填充系统的先验估计，$ \ mathbb {r}^{n} $ with $ n \ geq3 $
Uniform a priori estimates for $n$-th order Lane-Emden system in $\mathbb{R}^{n}$ with $n\geq3$
论文作者
论文摘要
在本文中，我们建立了统一的先验估计，该估计值是在任意维度的Navier边界条件$ n \ geq3 $的有限域中（较高）临界顺序超线性巷填充系统的阳性解决方案。首先，我们通过以局部方式移动平面的方法来证明沿边界附近的内向正常方向的奇数（高阶分数系统），甚至订单系统（整数订单系统）的单调性。然后，我们通过建立$ u $，$ v $，$-ΔU$和$-ΔV$之间的准确关系来得出统一的先验估计。我们的结果将[18，19]中关键顺序问题的先验估计从$ n = 2 $扩展到更高尺寸$ n \ geq3 $，而[6，8]中的统一估计值从一个方程式到系统。有了这样的先验估计，人们将能够通过拓扑度理论或持续论证获得解决方案的存在。
In this paper, we establish uniform a priori estimates for positive solutions to the (higher) critical order superlinear Lane-Emden system in bounded domains with Navier boundary conditions in arbitrary dimensions $n\geq3$. First, we prove the monotonicity of solutions for odd order (higher order fractional system) and even order system (integer order system) respectively along the inward normal direction near the boundary by the method of moving planes in local ways. Then we derive uniform a priori estimates by establishing the precise relationships between the maxima of $u$, $v$, $-Δu$ and $-Δv$ through Harnack inequality. Our results extended the uniform a priori estimates for critical order problems in [18, 19] from $n=2$ to higher dimensions $n\geq3$ and in [6, 8] from one single equation to system. With such a priori estimates, one will be able to obtain the existence of solutions via topological degree theory or continuation argument.
