论文标题
在双曲线填充物上存在一阶Sobolev空间的痕迹的表征
Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings
论文作者
论文摘要
在本文中，我们研究了配备加倍措施的紧凑型公制空间$ z $的双曲线填充$ x $的Sobolev空间的痕迹。鉴于$ x $的合适度量，我们可以将$ z $视为$ x $的边界。通过$ z $和欧几里得弧长度将$ x $与加权度量$μ$配置为加权度量$μ$，我们为一阶Sobolev空间的痕迹提供了特征。
In this paper, we study the existence of traces for Sobolev spaces on the hyperbolic filling $X$ of a compact metric space $Z$ equipped with a doubling measure. Given a suitable metric on $X$, we can regard $Z$ as the boundary of $X$. After equipping $X$ with a weighted measure $μ$ via the measure on $Z$ and the Euclidean arc length, we give characterizations for the existence of traces for first-order Sobolev spaces.
