English

On the best constant in {G}affney inequality

Functional Analysis 2025-04-02 v1

Abstract

We discuss the value of the best constant in Gaffney inequality namely \lVert \nabla \omega \rVert_{L^{2}}^{2}\leq C\left( \lVert d\omega\rVert_{L^{2}}^{2}+\lVert \delta\omega\rVert_{L^{2}% }^{2}+\lVert \omega\rVert_{L^{2}}^{2}\right) when either νω=0\nu\wedge\omega=0 or νω=0\nu\,\lrcorner\,\omega=0 on Ω.\partial\Omega.

Keywords

Cite

@article{arxiv.1712.04875,
  title  = {On the best constant in {G}affney inequality},
  author = {Gyula Csato and Bernard Dacorogna and Swarnendu Sil},
  journal= {arXiv preprint arXiv:1712.04875},
  year   = {2025}
}