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ISSN 1088-6826(e) ISSN 0002-9939(p)

Whitney property in two dimensional Sobolev spaces

Author(s): Dorin Bucur; Alessandro Giacomini; Paola Trebeschi
Journal: Proc. Amer. Math. Soc. 136 (2008), 2535-2545.
MSC (2000): Primary 46E35
Posted: March 4, 2008
MathSciNet review: 2390524
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Abstract: For , we prove that all the functions of $W_{\rm loc}^{2,p}(\mathbb{R}^2)$ satisfy the Whitney property; i.e., if $u \in W_{\rm loc}^{2,p}(\mathbb{R}^2)$ is such that $\nabla u=0$ (in the sense of capacity) on a connected set $K\subseteq \mathbb{R}^2$ , then is constant on .

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