The Monge-Ampère constraint: matching of isometries, density and regularity, and elastic theories of shallow shells

DOI10.1016/j.anihpc.2015.08.005zbMath1359.35085OpenAlexW2233044399MaRDI QIDQ501537

Marta Lewicka, L. Mahadevan, Mohammad Reza Pakzad

Publication date: 9 January 2017

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2015.08.005

zbMATH Keywords

nonlinear elasticitycalculus of variationsMonge-Ampère equationshallow shellsGamma convergenceisometric continuation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elasticity (74B20) Shells (74K25) Rigidity results (53C24) PDEs in connection with mechanics of deformable solids (35Q74) Monge-Ampère equations (35J96)

Related Items (16)

Plates with incompatible prestrain ⋮ The mathematics of thin structures ⋮ On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation ⋮ Geometry, analysis, and morphogenesis: Problems and prospects ⋮ Gaussian curvature as an identifier of shell rigidity ⋮ On asymptotic rigidity and continuity problems in nonlinear elasticity on manifolds and hypersurfaces ⋮ Plates with incompatible prestrain of high order ⋮ Relative bending energy for weakly prestrained shells ⋮ Derivation of a homogenized bending-torsion theory for rods with micro-heterogeneous prestrain ⋮ Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models ⋮ Convex integration for the Monge-Ampère equation in two dimensions ⋮ On the Korn Interpolation and Second Inequalities in Thin Domains ⋮ A local and global well-posedness results for the general stress-assisted diffusion systems ⋮ Derivation of von Kármán plate theory in the framework of three-dimensional viscoelasticity ⋮ Visualization of the convex integration solutions to the Monge-Ampère equation ⋮ Variational Problems for Föppl--von Kármán Plates

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
• An introduction to differential geometry with applications to elasticity
• Morphogenesis of thin hyperelastic plates: A constitutive theory of biological growth in the Föppl-von Kármán limit
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• Regularity properties of deformations with finite energy
• Weakly monotone functions
• Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells
• Plate theory for stressed heterogeneous multilayers of finite bending energy
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• Regularity properties of isometric immersions
• Continuation of Infinitesimal Bendings on Developable Surfaces and Equilibrium Equations for Nonlinear Bending Theory of Plates
• The shape of a long leaf
• The Föppl-von Kármán equations for plates with incompatible strains
• Sharp regularity results on second derivatives of solutions to the Monge-Ampère equation with VMO type data
• Strict convexity, strong ellipticity, and regularity in the calculus of variations
• On Mappings with Integrable Dilatation
• Lusin's condition (N) and mappings of the class W1, n.
• Theory of Shell Structures
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• The Infinite Hierarchy of Elastic Shell Models: Some Recent Results and a Conjecture
• ON ISOMETRIC IMMERSIONS OF A RIEMANNIAN SPACE WITH LITTLE REGULARITY
• The Weyl and Minkowski problems in differential geometry in the large

This page was built for publication: The Monge-Ampère constraint: matching of isometries, density and regularity, and elastic theories of shallow shells