Rough traces of $BV$ functions in metric measure spaces

Annales Fennici Mathematici, 46(1), 309-333 (2021) Following a Maz'ya-type approach, we adapt the theory of rough traces of functions of bounded variation ($BV$) in the context of doubling metric measure spaces supporting a Poincar\'e inequality. This eventually allows for an integration b...

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Bibliographic Details
Main Authors Buffa, Vito, MirandaJr, Michele
Format Journal Article
LanguageEnglish
Published 02.07.2019
Subjects
Mathematics - Analysis of PDEs
Mathematics - Functional Analysis
Mathematics - Metric Geometry
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Summary:Annales Fennici Mathematici, 46(1), 309-333 (2021) Following a Maz'ya-type approach, we adapt the theory of rough traces of functions of bounded variation ($BV$) in the context of doubling metric measure spaces supporting a Poincar\'e inequality. This eventually allows for an integration by parts formula involving the rough trace of such a function. We then compare our analysis with the discussion done in a recent work by P. Lahti and N. Shanmugalingam, where traces of $BV$ functions are studied by means of the more classical Lebesgue-point characterization, and we determine the conditions under which the two notions coincide.
DOI:10.48550/arxiv.1907.01673