Geodesic
Rough traces of BV functions in metric measure spaces
Vito Buffa1 ; Michele Miranda Jr.2
1 Bologna, Italy
2 University of Ferrara, Department of Mathematics and Computer Science
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 309-333

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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.
Keywords: Functions of bounded variation, metric measure spaces, traces, integration by parts formulas

Vito Buffa 1 ; Michele Miranda Jr. 2

1 Bologna, Italy
2 University of Ferrara, Department of Mathematics and Computer Science 
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Vito Buffa; Michele Miranda Jr. Rough traces of BV functions in metric measure spaces. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 309-333. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a16/