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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Whitney property in two dimensional Sobolev spaces


Authors: Dorin Bucur, Alessandro Giacomini and Paola Trebeschi
Journal: Proc. Amer. Math. Soc. 136 (2008), 2535-2545
MSC (2000): Primary 46E35
Published electronically: March 4, 2008
MathSciNet review: 2390524
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Abstract: For $ p >1$, 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 $ u$ is constant on $ K$.


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Additional Information

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: http://dx.doi.org/10.1090/S0002-9939-08-09366-0
PII: S 0002-9939(08)09366-0
Received by editor(s): May 15, 2007
Published electronically: March 4, 2008
Communicated by: Mario Bonk
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.