Hölder domains and the boundary Harnack principle
Hölder domains and the boundary Harnack principle
复制标题
Hölder 域和边界 Harnack 原理
DOI：
--
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
K. Burdzy
中科院分区：
文献类型：
--
作者：
R. Bañuelos;R. Bass;K. Burdzy
常数c仅通过下面（1）中定义的常数cL依赖于L。当然，c也取决于D，V和K。上述结果表明，边界Harnack原理在所有的保持器区域都成立. Bass和Burdzy（1990 a）首先证明了α ∈（1/2，1]）的范围，定理3.5和4.5。后来Banuelos（未发表）将其推广到α的整个范围，只要区域在边界上也满足一致容量条件。在Banuelos（1990）中，引入了一类称为β阶一致保持器域的域.通过定理1的证明的一种变形，可以得到这类域的边界Harnack原理（对所有β ∈（0，1））.为了使本说明简洁，我们参考
The constant c depends on L only through the constant cL defined in (1) below. Of course, c also depends on D, V and K. The above result shows that the boundary Harnack principle holds in all Holder domains. It was first proven for the range α ∈ (1/2, 1] by Bass and Burdzy (1990a), Theorems 3.5 and 4.5. It was subsequently extended by Banuelos (unpublished) to the full range of α provided the domain also satisfies a uniform capacity condition on the boundary. In Banuelos (1990) a class of domains called uniformly Holder domains of order β was introduced. A boundary Harnack principle may be obtained for such domains (for all β ∈ (0, 1)) by a variation of the proof of Theorem 1. In order to make this note compact, we refer