134 research outputs found
Rigidity and regularity of co-dimension one Sobolev isometric immersions
We prove the developability and regularity of isometric
immersions of -dimensional domains into . As a conclusion we show
that any such Sobolev isometry can be approximated by smooth isometries in the
strong norm, provided the domain is and convex. Both results
fail to be true if the Sobolev regularity is weaker than .Comment: 43 pages, 15 figure
Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells
We perform a detailed analysis of first order Sobolev-regular infinitesimal
isometries on developable surfaces without affine regions. We prove that given
enough regularity of the surface, any first order infinitesimal isometry can be
matched to an infinitesimal isometry of an arbitrarily high order. We discuss
the implications of this result for the elasticity of thin developable shells
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