Extensions and traces of functions of bounded variation on metric spaces

摘要

In the setting of a metric space equipped with a doubling measure and supporting a Poincare inequality, and based on results by Bjorn 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. (C) 2014 Elsevier Inc. All rights reserved.