The divergence theorem and nonlocal counterparts
Analysis of PDEs
2024-03-06 v3
Abstract
We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence and the normal derivative. We employ these to provide definitions of well-known nonlocal concepts such as the fractional perimeter.
Cite
@article{arxiv.2302.01945,
title = {The divergence theorem and nonlocal counterparts},
author = {Solveig Hepp and Moritz Kassmann},
journal= {arXiv preprint arXiv:2302.01945},
year = {2024}
}
Comments
In the final version we have explained how to apply our proof of the divergence theorem to more general domains including polytopes. The article will be published in the Bulletin of the London Mathematical Society