# American Institute of Mathematical Sciences

July  2010, 9(4): 987-1010. doi: 10.3934/cpaa.2010.9.987

## Coercive energy estimates for differential forms in semi-convex domains

 1 Department of Mathematics, University of Missouri, Columbia, MO 65211, United States, United States 2 Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester MA 01609-2280, United States 3 Department of Mathematics, Zhongshan University, Guangzhou, 510275, China

Received  July 2009 Revised  February 2010 Published  April 2010

In this paper, we prove a $H^1$-coercive estimate for differential forms of arbitrary degrees in semi-convex domains of the Euclidean space. The key result is an integral identity involving a boundary term in which the Weingarten matrix of the boundary intervenes, established for any Lipschitz domain $\Omega\subseteq \mathcal{R}^n$ whose outward unit normal $\nu$ belongs to $L^{n-1}_1(\partial\Omega)$, the $L^{n-1}$-based Sobolev space of order one on $\partial\Omega$.
Citation: Dorina Mitrea, Irina Mitrea, Marius Mitrea, Lixin Yan. Coercive energy estimates for differential forms in semi-convex domains. Communications on Pure & Applied Analysis, 2010, 9 (4) : 987-1010. doi: 10.3934/cpaa.2010.9.987
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