preprint

Inserted: 12 nov 2021

Year: 2017

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 $\nu\wedge\omega=0$ or $\nu\,\lrcorner\,\omega=0$ on $\partial\Omega.$