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

DOI10.1016/j.bulsci.2007.05.004zbMath1148.35004arXivmath/0507310OpenAlexW2079440723MaRDI QIDQ924911

Omar Anza Hafsa, Jean-Philippe Mandallena

Publication date: 29 May 2008

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507310

zbMATH Keywords

dimensional reductiondeterminant conditionnonlinear membrane energy

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Variational methods applied to PDEs (35A15) Membranes (74K15)

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Cites Work

• Unnamed Item
• Unnamed Item
• The nonlinear membrane energy: variational derivation under the constraint ``\(\det \nabla u\neq 0\)
• An introduction to \(\Gamma\)-convergence
• Construction of nonsingular isoperimetric films
• Interchange of infimum and integral
• The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
• MODELING OF A MEMBRANE FOR NONLINEARLY ELASTIC INCOMPRESSIBLE MATERIALS VIA GAMMA-CONVERGENCE
• Optimal design and relaxation of variational problems, II
• Partial Differential Relations
• Une méthode de Γ-convergence pour un modèle de membrane non linéaire
• Relaxation of singular functionals defined on Sobolev spaces
• Set-valued analysis