no. 3-4
Differential Geometry
Approximating W2,2 isometric immersions
[Approximation de W2,2 par des immersions isométriques]
Présenté par : John M. Ball
Hornung, Peter1
1 Fachbereich Mathematik, Universität Duisburg-Essen, 47048 Duisburg, Germany
Comptes Rendus. Mathématique, Tome 346 (2008) no. 3-4, pp. 189-192

Let S⊂R2 be a bounded Lipschitz domain and set Wiso2,2(S;R3)={u∈W2,2(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 S⊂R2 un domaine lipschitzien borné et Wiso2,2(S;R3) l'ensemble Wiso2,2(S;R3)={u∈W2,2(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).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.01.001

Hornung, Peter 1

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

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