# On the boundary conditions in estimating $\nabla ω$ by div $ω$ and curl $ω.$

created by csato on 12 Nov 2021

[BibTeX]

preprint

Inserted: 12 nov 2021

Year: 2017

ArXiv: 1709.06117 PDF

Abstract:

In this paper we study under what boundary conditions the inequality $$\ \nabla\omega\ {L2(\Omega)}2\leq C\left(\ {\rm curl}\omega\ {L2(\Omega)}2+ \ {\rm div}\omega\ {L2(\Omega)}2+\ \omega\ {L2(\Omega)}2\right)$$ holds true. It is known that such an estimate holds if either the tangential or normal component of $\omega$ vanishes on the boundary $\partial\omega.$ We show that the vanishing tangential component condition is a special case of a more general one. In two dimensions we give an interpolation result between these two classical boundary conditions.

Credits | Cookie policy | HTML 5 | CSS 2.1