On the best constant in {G}affney inequality

Abstract

We discuss the value of the best constant in Gaffney inequality namely $$ \lVert \nabla ω\rVert_{L^{2}}^{2}\leq C\left( \lVert dω\rVert_{L^{2}}^{2}+\lVert δω\rVert_{L^{2}% }^{2}+\lVert ω\rVert_{L^{2}}^{2}\right) $$ when either $\nu \wedge \omega =0$ or $\nu ┘\omega =0$ on $\partial \Omega .$

References in corpus (1)

• On Korn's First Inequality for Tangential or Normal Boundary Conditions with Explicit Constants

Cited by in corpus (2)

• Sobolev-Gaffney type inequalities for differential forms on sub-Riemannian contact manifolds with bounded geometry
• Friedrichs inequality in irregular domains