The nonlinear membrane energy: variational derivation under the constraint ``\(\det \nabla u\neq 0\)

DOI10.1016/J.MATPUR.2006.01.004zbMath1114.35003OpenAlexW2041217130MaRDI QIDQ869108

Omar Anza Hafsa, Jean-Philippe Mandallena

Publication date: 26 February 2007

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2006.01.004

zbMATH Keywords

dimensional reduction\(\Gamma\)-convergencedeterminant constraint

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Energy minimization in equilibrium problems in solid mechanics (74G65) Variational methods applied to PDEs (35A15) Existence theories for free problems in two or more independent variables (49J10) Membranes (74K15)

Related Items (6)

Remarks on homogenization and \(3D\)-\(2D\) dimension reduction of unbounded energies on thin films ⋮ Brittle membranes in finite elasticity ⋮ The nonlinear membrane energy: Variational derivation under the constraint ``det\(\nabla u>\)0 ⋮ Relaxation theorems in nonlinear elasticity ⋮ A relaxation process for bifunctionals of displacement-Young measure state variables: a model of multi-material with micro-structured strong interface ⋮ On the theory of relaxation in nonlinear elasticity with constraints on the determinant

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