论文标题
带状域中的均匀分数Sobolev空间的痕迹
Trace of Homogeneous Fractional Sobolev Spaces on Strip-like Domains
论文作者
论文摘要
在本文中，我们讨论了在无限条状域上的均匀分数Sobolev空间的痕量操作员。我们确定轨迹空间上的固有半静电剂，该拟量空间允许右逆。固有的静物包括先前用于描述均匀Sobolev空间的痕迹的两个特征，这是痕迹的两个断开组件与筛选的Sobolev Eminorm之间的关系。但是，与其均匀的sobolev空间等效不同，分数Sobolev空间需要屏幕上的Sobolev Seminorm，该sobolev seminorm捕获了分数Sobolev空间的非本地性质。我们研究了这个新的远筛选的Sobolev空间之间的一些基本关系，并在先前讨论的筛选的Sobolev空间之间进行了研究。
In this paper, we discuss the trace operator for homogeneous fractional Sobolev spaces over infinite strip-like domains. We determine intrinsic seminorms on the trace space that allow for a bounded right inverse. The intrinsic seminorm includes two features previously used to describe the trace of homogeneous Sobolev spaces, a relation between the two disconnected components of the trace and the screened Sobolev seminorm. However, unlike its homogeneous Sobolev space equivalent, fractional Sobolev spaces require a far screened Sobolev seminorm that captures the non-local properties of fractional Sobolev spaces. We study some basic relationships between this new far screened Sobolev space with previously discussed screened Sobolev spaces.
