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Communications on Pure and Applied Analysis (CPAA)
 

Coercive energy estimates for differential forms in semi-convex domains

Pages: 987 - 1010, Volume 9, Issue 4, July 2010      doi:10.3934/cpaa.2010.9.987

 
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Dorina Mitrea - Department of Mathematics, University of Missouri, Columbia, MO 65211, United States (email)
Irina Mitrea - Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester MA 01609-2280, United States (email)
Marius Mitrea - Department of Mathematics, University of Missouri, Columbia, MO 65211, United States (email)
Lixin Yan - Department of Mathematics, Zhongshan University, Guangzhou, 510275, China (email)

Abstract: 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, Weingarten map, differential forms, coercive estimates.
Mathematics Subject Classification:  Primary: 35B65, 35J46, 46E35; Secondary: 35B45, 35J50, 35J57, 53C45.

Received: July 2009;      Revised: February 2010;      Available Online: April 2010.