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arXiv · 2208.10812

Representation formulas for pairings between divergence-measure fields and $BV$ functions

Giovanni E. Comi·Graziano Crasta·Virginia De Cicco·Annalisa Malusa
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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 In particular, we extend a representation formula from an unpublished paper of Anzellotti [7] involving the limit of cylindrical averages for normal traces, and we exploit a result of [35] in order to derive another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.

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Giovanni E. Comi, Graziano Crasta, Virginia De Cicco, Annalisa Malusa. 2022-08-23. Representation formulas for pairings between divergence-measure fields and $BV$ functions. https://arxiv.org/abs/2208.10812

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