English

Some nonlocal formulas inspired by an identity of James Simon

Analysis of PDEs 2025-07-31 v3

Abstract

Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. Our formula also recovers the classical case in the limit, thus providing an approach to Simons' work that does not heavily rely on differential geometry.

Keywords

Cite

@article{arxiv.2306.15179,
  title  = {Some nonlocal formulas inspired by an identity of James Simon},
  author = {Serena Dipierro and Jack Thompson and Enrico Valdinoci},
  journal= {arXiv preprint arXiv:2306.15179},
  year   = {2025}
}