Coercive energy estimates for differential forms in semi-convex domains
Dorina Mitrea, Irina Mitrea, Marius Mitrea, Lixin Yan · Communications on Pure & Applied Analysis · 2010
In this paper, we prove a $H^1$-coercive estimate for differentialforms of arbitrary degrees in semi-convex domains of the Euclidean space.The key result is an integral identity involving a boundary term in whichthe Weingarten matrix of the boundary intervenes, establishedfor any Lipschitz domain $\Omega\subseteq \mathcal{R}^n$ whoseoutward unit normal $ u$ belongs to $L^{n-1}_1(\partial\Omega)$,the $L^{n-1}$-based Sobolev space of order one on $\partial\Omega$.