Calculus of Variations and Geometric Measure Theory
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V. Buffa - M. Miranda Jr

Rough traces of $BV$ functions in metric measure spaces

created by buffa on 04 Jul 2019
modified on 04 Jan 2022


Published Paper

Inserted: 4 jul 2019
Last Updated: 4 jan 2022

Journal: Annales Fennici Mathematici
Year: 2021
Doi: 10.5186/aasfm.2021.4625

ArXiv: 1907.01673 PDF


Following a Maz'ya-type approach, we re-adapt the theory of rough traces of functions of bounded variation ($BV$) in 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 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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