# Rough Traces of $BV$ Functions in Metric Measure Spaces

created by buffa on 23 Jan 2019
modified on 28 Jan 2019

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Preprint

Inserted: 23 jan 2019
Last Updated: 28 jan 2019

Year: 2019

Abstract:

Following a Maz’ya-type approach, we re-adapt the theory of rough traces of BV functions in the context of doubling metric measure spaces supporting a Poincaré inequality. This eventually allows for a Gauss-Green type formula involving indeed 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.