# Regularity of intrinsically convex $H^2$ surfaces and the derivation of homogenized bending shell models

We prove smoothness of $H^2$ isometric immersions of surfaces endowed with a smooth Riemannian metric of positive Gauss curvature. We use this regularity result to rigorously derive homogenized bending models of convex shells from three-dimensional nonlinear elasticity.

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**Affiliations:**

^{1}IMT,

^{2}IRMAR,

^{3}LJLL

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