English

A generalization of Gauss' divergence theorem

Analysis of PDEs 2015-03-10 v2

Abstract

This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is that they are based on a non Archimedean field namely on a field which contains infinite and infinitesimal numbers. Ultrafunctions have been introduced to provide generalized solutions to equations which do not have any solutions not even among the distributions.

Keywords

Cite

@article{arxiv.1406.4349,
  title  = {A generalization of Gauss' divergence theorem},
  author = {Vieri Benci and Lorenzo Luperi Baglini},
  journal= {arXiv preprint arXiv:1406.4349},
  year   = {2015}
}

Comments

arXiv admin note: text overlap with arXiv:1405.4152

R2 v1 2026-06-22T04:40:16.667Z