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

Coercive energy estimates for differential forms in semi-convex domains

Dorina Mitrea 1, , Irina Mitrea 2, , Marius Mitrea 1, and  Lixin Yan 3,

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 $\partial\Omega$.
Keywords: Semi-convex domains, differential forms, Weingarten map, coercive estimates..
Mathematics Subject Classification: Primary: 35B65, 35J46, 46E35; Secondary: 35B45, 35J50, 35J57, 53C4.
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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