Regularity of intrinsically convex $W^{2,2}$ surfaces and a derivation of a homogenized bending theory of convex shells

Peter Hornung; Igor Velcic

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arXiv · 1506.02571

Regularity of intrinsically convex $W^{2,2}$ surfaces and a derivation of a homogenized bending theory of convex shells

Peter Hornung·Igor Velcic

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Abstract

We prove smoothness of $W^{2,2}$ isometric immersions of surfaces endowed with a smooth Riemannian metric of positive Gauss curvature. We then derive the $\Gamma$-limit of three dimensional nonlinear shells with inhomogeneous energy density, in the bending energy regime.

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Peter Hornung, Igor Velcic. 2015-06-08. Regularity of intrinsically convex $W^{2,2}$ surfaces and a derivation of a homogenized bending theory of convex shells. https://arxiv.org/abs/1506.02571

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