Extensions and traces of functions of bounded variation on metric spaces
Research output: Contribution to journal › Article › Scientific › peer-review
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) , 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) . 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.
|Number of pages||17|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2015|
|MoE publication type||A1 Journal article-refereed|
- Boundary trace, Bounded variation, Extension, Jump set, Locality, Uniform domain