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

被引：6

作者：

Hornung, Peter ^{[1
]}

Velcic, Igor ^{[2
]}

机构：

[1] Tech Univ Dresden, Fak Math, D-01062 Dresden, Germany

[2] Univ Zagreb, Fac Elect Engn & Comp, Unska 3, Zagreb, Croatia

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2018年 / 115卷

关键词：

Nonlinear elasticity; Isometric immersions; Homogenization; Positive Gauss curvature; Dimension reduction; Bending theory; 3D NONLINEAR ELASTICITY; PLATE-THEORY; 3-DIMENSIONAL ELASTICITY; GAMMA-CONVERGENCE; ENERGY; MODEL; EQUATION; LIMIT;

D O I：

10.1016/j.matpur.2018.04.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove interior regularity for W-2,W-2 isometric immersions of surfaces endowed with a smooth Riemannian metric of positive Gauss curvature. We then derive the P-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. (C) 2018 Published by Elsevier Masson SAS.

引用

页码：1 / 23

页数：23

共 5 条

[1] A note on Sobolev isometric immersions below W2,2 regularity
Liu, Zhuomin
Maly, Jan
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2017, 52 : 1 - 10
[2] On global W2,δ stimates for the Monge-Ampère equation on general bounded convex domains
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[J]. PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 5 (04):
[3] On the C1,γ ((Ω)over-bar) ∧ W2,2 (Ω) regularity for a class of electro-rheological fluids
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[4] On the Existence, Uniqueness and C1,γ((Ω)over-bar) ∧ W2,2(Ω) Regularity for a Class of Shear-Thinning Fluids
Crispo, Francesca
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[5] On global W2,δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W^{2,\delta }$$\end{document} estimates for the Monge–Ampère equation on general bounded convex domains
Nam Q. Le
[J]. Partial Differential Equations and Applications, 2024, 5 (4):

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