Extensions and traces of functions of bounded variation on metric spaces

Panu Lahti*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)521-537
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume423
Issue number1
DOIs
Publication statusPublished - 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • Boundary trace
  • Bounded variation
  • Extension
  • Jump set
  • Locality
  • Uniform domain

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