Coercive energy estimates for differential forms in semi-convex domains

Dorina Mitrea; Irina Mitrea; Marius Mitrea; Lixin Yan

doi:10.3934/cpaa.2010.9.987

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2010, Volume 9, Issue 4: 987-1010. Doi: 10.3934/cpaa.2010.9.987

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Coercive energy estimates for differential forms in semi-convex domains

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

Received: July 2009

Revised: February 2010

Published: July 2010

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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 $\partial\Omega$.

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Mathematics Subject Classification: Primary: 35B65, 35J46, 46E35; Secondary: 35B45, 35J50, 35J57, 53C45.

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