Rough traces of BV functions in metric measure spaces

Abstract

Following a Maz'ya-type approach, we adapt the theory of rough traces of functions of bounded variation (BV) to the context of doubling metric measure spaces supporting a Poincaré inequality. This eventually allows for an integration by parts formula involving the rough trace of such functions. We then compare our analysis with the study done in a recent work by Lahti and 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.