Regularity of intrinsically convex W2,2 surfaces and a derivation of a homogenized bending theory of convex shells

We prove interior regularity for W2,2 isometric immersions of surfaces endowed with a smooth Riemannian metric of positive Gauss curvature. We then derive the Γ-limit of three dimensional nonlinear shells with inhomogeneous energy density, in the bending energy regime. This derivation is incomplete...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées 2018-07, Vol.115, p.1-23
Main Authors: Hornung, Peter, Velčić, Igor
Format: Article
Language:English
Subjects:
Bending theory
Dimension reduction
Homogenization
Isometric immersions
Nonlinear elasticity
Positive Gauss curvature
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Summary:We prove interior regularity for W2,2 isometric immersions of surfaces endowed with a smooth Riemannian metric of positive Gauss curvature. We then derive the Γ-limit of three dimensional nonlinear shells with inhomogeneous energy density, in the bending energy regime. This derivation is incomplete in that it requires an additional technical hypothesis. Nous prouvons un résultat de régularité intérieure pour des immersions isometriques W2,2 de surfaces munies d'une metrique riemannienne reguliere de courbure de Gauss positive. Nous derivons la Γ-limite de coques en flexion non linéaires et non homogènes. Ce résultat est incomplet puisqu'il nécessite une hypothèse (technique) additionnelle.
ISSN:0021-7824
DOI:10.1016/j.matpur.2018.04.008