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arXiv · 1907.01673

Rough traces of $BV$ functions in metric measure spaces

Vito Buffa·Michele Miranda Jr
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Abstract

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.

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Vito Buffa, Michele Miranda Jr. 2019-07-02. Rough traces of $BV$ functions in metric measure spaces. https://doi.org/10.5186/aasfm.2021.4625

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