Mathematical Analysis/Partial Differential Equations
A case of density in W2,p(M;N)
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 735-740.

Given two compact Riemannian manifolds Mm,Nn without boundary and m12p<m, we show that maps which are smooth except on finitely many points are dense in W2,p(M;N). If, in addition, πm1(N) is trivial, then C(M;N) is dense in W2,p(M;N).

On considère deux variétés riemaniennes compactes sans bord Mm et Nn. Quand m12p<m, on montre que les fonctions lisses sauf en un nombre fini de points sont denses dans W2,p(M;N). Si la variété N vérifie πm1(N)={0}, alors C(M;N) est dense dans W2,p(M;N).

Accepted:
Published online:
DOI: 10.1016/j.crma.2008.05.006
Bousquet, Pierre 1; Ponce, Augusto C. 2; Van Schaftingen, Jean 3

1 Unité de mathématiques pures et appliquées (UMR CNRS 5669), ENS Lyon, 46, allée d'Italie, 69007 Lyon, France
2 Laboratoire de mathématiques et physique théorique (UMR CNRS 6083), Université de Tours, 37200 Tours, France
3 Département de mathématique, Université catholique de Louvain, chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgique
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Bousquet, Pierre; Ponce, Augusto C.; Van Schaftingen, Jean. A case of density in $ {W}^{2,p}(M;N)$. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 735-740. doi : 10.1016/j.crma.2008.05.006. http://www.numdam.org/articles/10.1016/j.crma.2008.05.006/

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