Trace theorems for functions of bounded variation in metric spaces

P. Lahti, N. Shanmugalingam*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

Abstract

In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a 1-Poincaré inequality, and obtain L1 estimates of the trace functions. In contrast with the treatment of traces given in other papers on this subject, the traces we consider do not require knowledge of the function in the exterior of the domain. We also establish a Maz'ya-type inequality for functions of bounded variation that vanish on a set of positive capacity.

Original languageEnglish
Pages (from-to)2754-2791
Number of pages38
JournalJournal of Functional Analysis
Volume274
Issue number10
DOIs
Publication statusPublished - 15 May 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • BV function
  • Capacitary inequality
  • Discrete convolution
  • Trace

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