Comptes Rendus
Differential Geometry
Approximating W2,2 isometric immersions
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 189-192.

Let SR2 be a bounded Lipschitz domain and set Wiso2,2(S;R3)={uW2,2(S;R3):(u)T(u)=Id a.e.}. Under an additional regularity condition on the boundary ∂S (which is satisfied if it is piecewise continuously differentiable) we prove that the W2,2 closure of Wiso2,2(S;R3)C(S¯;R3) agrees with Wiso2,2(S;R3).

Soient SR2 un domaine lipschitzien borné et Wiso2,2(S;R3) l'ensemble Wiso2,2(S;R3)={uW2,2(S;R3):(u)T(u)=Id p.p.}. Sous une hypothèse supplémentaire de régularité sur la frontière ∂S (qui est satisfaite dans le cas où ∂S est continument différentiable par morceaux), nous prouvons que l'adhérence W2,2 de Wiso2,2(S;R3)C(S¯;R3) est Wiso2,2(S;R3).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.01.001

Peter Hornung 1

1 Fachbereich Mathematik, Universität Duisburg-Essen, 47048 Duisburg, Germany
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Peter Hornung. Approximating $ {W}^{2,2}$ isometric immersions. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 189-192. doi : 10.1016/j.crma.2008.01.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.01.001/

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