Let be a bounded Lipschitz domain and set . Under an additional regularity condition on the boundary ∂S (which is satisfied if it is piecewise continuously differentiable) we prove that the closure of agrees with .
Soient un domaine lipschitzien borné et l'ensemble . 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 de est .
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Peter Hornung 1
@article{CRMATH_2008__346_3-4_189_0, author = {Peter Hornung}, title = {Approximating $ {W}^{2,2}$ isometric immersions}, journal = {Comptes Rendus. Math\'ematique}, pages = {189--192}, publisher = {Elsevier}, volume = {346}, number = {3-4}, year = {2008}, doi = {10.1016/j.crma.2008.01.001}, language = {en}, }
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/
[1] Singularities and computation of minimizers for variational problems, London Math. Soc. Lecture Note Ser., vol. 284, 2001, pp. 1-20
[2] Derivation of a plate theory for incompressible materials, C. R. Acad. Sci. Paris, Ser. I, Volume 344 (2007), pp. 541-544
[3] Rigorous derivation of nonlinear plate theory and geometric rigidity, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002), pp. 173-178
[4] A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity, Comm. Pure Appl. Math., Volume 55 (2002), pp. 1461-1506
[5] P. Hornung, A density result for isometric immersions, preprint, available under http://analysis.math.uni-duisburg.de/publications/preprints/Hornung4.pdf
[6] B. Kirchheim, Geometry and rigidity of microstructures, Habilitation thesis, University of Leipzig, 2001
[7] Regularity properties of isometric immersions, Math. Z., Volume 251 (2005) no. 2, pp. 313-331
[8] On the Sobolev space of isometric immersions, J. Differential Geom., Volume 66 (2004) no. 1, pp. 47-69
[9] Une justification partielle du modèle de plaque en flexion par Γ-convergence, C. R. Acad. Sci. Paris, Ser. I, Volume 332 (2001), pp. 587-592
[10] On the justification of the nonlinear inextensional plate model, Arch. Ration. Mech. Anal., Volume 167 (2003), pp. 179-209
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