2019
DOI: 10.48550/arxiv.1906.07432
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On $BV$ functions and essentially bounded divergence-measure fields in metric spaces

Abstract: By employing the differential structure recently developed by N. Gigli, we can extend the notion of divergence-measure vector fields DM p (X), 1 ≤ p ≤ ∞, to the very general context of a (locally compact) metric measure space (X, d, µ) satisfying no further structural assumptions. Here we determine the appropriate class of domains for which it is possible to obtain a Gauss-Green formula in terms of the normal trace of a DM ∞ (X) vector field. This differential machinery is also the natural framework to special… Show more

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Cited by 6 publications
(28 citation statements)
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“…Gauss-Green integration by parts formulae for sets of finite perimeter and vector fields with such low regularity in the Euclidean setting have been studied in [CTZ09,CP20]. Later on, in [BCM19] the theory has been partially extended to locally compact RCD(K, ∞) metric measure spaces (see also the recent [Br21]). Here, fully exploiting the finite dimensionality assumption N < ∞ and the regularity theory for sets of finite perimeter, we achieve a quite complete extension of the Euclidean results, sharpening those in [BCM19].…”
Section: Pointwise Behaviour Of the Unit Normal And Operations With S...mentioning
confidence: 99%
See 4 more Smart Citations
“…Gauss-Green integration by parts formulae for sets of finite perimeter and vector fields with such low regularity in the Euclidean setting have been studied in [CTZ09,CP20]. Later on, in [BCM19] the theory has been partially extended to locally compact RCD(K, ∞) metric measure spaces (see also the recent [Br21]). Here, fully exploiting the finite dimensionality assumption N < ∞ and the regularity theory for sets of finite perimeter, we achieve a quite complete extension of the Euclidean results, sharpening those in [BCM19].…”
Section: Pointwise Behaviour Of the Unit Normal And Operations With S...mentioning
confidence: 99%
“…Later on, in [BCM19] the theory has been partially extended to locally compact RCD(K, ∞) metric measure spaces (see also the recent [Br21]). Here, fully exploiting the finite dimensionality assumption N < ∞ and the regularity theory for sets of finite perimeter, we achieve a quite complete extension of the Euclidean results, sharpening those in [BCM19].…”
Section: Pointwise Behaviour Of the Unit Normal And Operations With S...mentioning
confidence: 99%
See 3 more Smart Citations