Proceedings of the American Mathematical Society

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
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46E35

Dorin Bucur
Affiliation: Laboratoire de Mathématiques, CNRS UMR 5127 Université de Savoie, Campus Scientifique, 73376 Le-Bourget-Du-Lac, France
Email: dorin.bucur@univ-savoie.fr

Alessandro Giacomini
Affiliation: Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy
Email: alessandro.giacomini@ing.unibs.it

Paola Trebeschi
Affiliation: Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy
Email: paola.trebeschi@ing.unibs.it

DOI: 10.1090/S0002-9939-08-09366-0
PII: S 0002-9939(08)09366-0
Received by editor(s): May 15, 2007
Posted: March 4, 2008
Communicated by: Mario Bonk
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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