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Whitney property in two dimensional Sobolev spaces

Authors:	Dorin Bucur Alessandro Giacomini Paola Trebeschi

Institution:	Laboratoire de Mathématiques, CNRS UMR 5127 Université de Savoie, Campus Scientifique, 73376 Le-Bourget-Du-Lac, France ; Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy ; Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy

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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