Anzellotti's pairing theory and the Gauss--Green theorem

Graziano Crasta; Virginia De Cicco

doi:10.1016/j.aim.2018.12.007

Anzellotti's pairing theory and the Gauss--Green theorem

Functional Analysis 2019-05-23 v2

Authors: Graziano Crasta , Virginia De Cicco

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Abstract

In this paper we obtain a very general Gauss-Green formula for weakly differentiable functions and sets of finite perimeter. This result is obtained by revisiting Anzellotti's pairing theory and by characterizing the measure pairing $(\boldsymbol{A}, Du)$ when $\boldsymbol{A}$ is a bounded divergence measure vector field and $u$ is a bounded function of bounded variation.

Keywords

Gauss-Green theorem Anzellotti pairing theory weakly differentiable functions sets of finite perimeter divergence measure vector field bounded variation measure pairing

Cite

@article{arxiv.1708.00792,
  title  = {Anzellotti's pairing theory and the Gauss--Green theorem},
  author = {Graziano Crasta and Virginia De Cicco},
  journal= {arXiv preprint arXiv:1708.00792},
  year   = {2019}
}

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27 pages

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