Representation formulas for pairings between divergence-measure fields and $BV$ functions
Abstract
The purpose of this paper is to find pointwise representation formulas for the density of the pairing between divergence-measure fields and BV functions, in this way continuing the research started in [17,20]. In particular, we extend a representation formula from an unpublished paper of Anzellotti [7] involving the limit of cylindrical averages for normal traces, and we exploit a result of [35] in order to derive another representation in terms of limits of averages in half balls.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.10812
- arXiv:
- arXiv:2208.10812
- Bibcode:
- 2022arXiv220810812C
- Keywords:
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- Mathematics - Functional Analysis;
- 26B30;
- 26B20;
- 49Q15
- E-Print:
- 24 pages