Extensions and traces of functions of bounded variation on metric spaces |
| |
Authors: | Panu Lahti |
| |
Affiliation: | Aalto University, School of Science, Department of Mathematics and Systems Analysis, P.O. Box 11100, FI-00076 Aalto, Finland |
| |
Abstract: | In the setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality, and based on results by Björn and Shanmugalingam (2007) [7], we show that functions of bounded variation can be extended from any bounded uniform domain to the whole space. Closely related to extensions is the concept of boundary traces, which have previously been studied by Hakkarainen et al. (2014) [17]. On spaces that satisfy a suitable locality condition for sets of finite perimeter, we establish some basic results for the traces of functions of bounded variation. Our analysis of traces also produces novel pointwise results on the behavior of functions of bounded variation in their jump sets. |
| |
Keywords: | Boundary trace Bounded variation Extension Jump set Locality Uniform domain |
本文献已被 ScienceDirect 等数据库收录! |
|