Rough traces of $BV$ functions in metric measure spaces
Metric Geometry
2021-07-20 v5 Analysis of PDEs
Functional Analysis
Abstract
Following a Maz'ya-type approach, we adapt the theory of rough traces of functions of bounded variation () 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 functions are studied by means of the more classical Lebesgue-point characterization, and we determine the conditions under which the two notions coincide.
Keywords
Cite
@article{arxiv.1907.01673,
title = {Rough traces of $BV$ functions in metric measure spaces},
author = {Vito Buffa and Michele Miranda},
journal= {arXiv preprint arXiv:1907.01673},
year = {2021}
}