Geodesic
A bounded linear extension operator for $L^{2,p}(\mathbb{R}^2)$
Arie Israel1
1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012
Annals of mathematics, Tome 178 (2013) no. 1, pp. 183-230.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $L^{2,p}(\mathbb{R}^2)$ be the Sobolev space of real-valued functions on the plane whose Hessian belongs to $L^p$. For any finite subset $E \subset \Bbb{R}^2$ and $p>2$, let $L^{2,p}(\Bbb{R}^2)|_E$ be the space of real-valued functions on $E$, equipped with the trace seminorm. In this paper we construct a bounded linear extension operator $T : L^{2,p}(\mathbb{R}^2)|_E \rightarrow L^{2,p}(\mathbb{R}^2)$. We also provide an explicit formula that approximates the $L^{2,p}(\mathbb{R}^2)|_E$ trace seminorm.
DOI : 10.4007/annals.2013.178.1.3

Arie Israel 1

1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 
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Arie Israel. A bounded linear extension operator for $L^{2,p}(\mathbb{R}^2)$. Annals of mathematics, Tome 178 (2013) no. 1, pp. 183-230. doi : 10.4007/annals.2013.178.1.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.1.3/

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