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Trace and Density Results on Regular Trees
Potential Analysis ( IF 1.1 ) Pub Date : 2021-03-06 , DOI: 10.1007/s11118-021-09907-2 Pekka Koskela , Khanh Ngoc Nguyen , Zhuang Wang
中文翻译:
规则树上的迹线和密度结果
更新日期:2021-03-07
Potential Analysis ( IF 1.1 ) Pub Date : 2021-03-06 , DOI: 10.1007/s11118-021-09907-2 Pekka Koskela , Khanh Ngoc Nguyen , Zhuang Wang
The boundary of a regular tree can be viewed as a Cantor-type set. We equip our tree with a weighted distance and a weighted measure via the Euclidean arc-length and consider the associated first-order Sobolev spaces. We give characterizations for the existence of traces and for the density of compactly supported functions.
中文翻译:
规则树上的迹线和密度结果
规则树的边界可以视为Cantor类型的集合。我们通过欧几里得弧长为树提供加权距离和加权度量,并考虑相关的一阶Sobolev空间。我们给出了痕迹的存在以及紧密支持的函数的密度的表征。