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In this paper we study under what boundary conditions the inequality$$\|\nabla\omega\|_{L^2(\Omega)}^2\leq C\left(\|{\rmcurl}\omega\|_{L^2(\Omega)}^2+ \|{\rmdiv}\omega\|_{L^2(\Omega)}^2+\|\omega\|_{L^2(\Omega)}^2\right) $$ holds true.It is known that such an estimate holds if either the tangential or normalcomponent of $\omega$ vanishes on the boundary $\partial\omega.$ We show thatthe vanishing tangential component condition is a special case of a moregeneral one. In two dimensions we give an interpolation result between thesetwo classical boundary conditions.

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