An estimate of the \(H^1\)-norm of deformations in terms of the \(L^1\)-norm of their Cauchy-Green tensors

DOI10.1016/j.crma.2004.01.014zbMath1183.74008OpenAlexW2071885755MaRDI QIDQ1433397

Philippe G. Ciarlet, Christinel Mardare

Publication date: 15 June 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2004.01.014

Mathematics Subject Classification ID

Kinematics of deformation (74A05)

Related Items

Another approach to linearized elasticity and Korn's inequality, LINEAR AND NONLINEAR KORN INEQUALITIES ON CURVES IN ℝ³, ON THE RECOVERY AND CONTINUITY OF A SUBMANIFOLD WITH BOUNDARY, ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Continuity of a deformation in \(H^{1}\) as a function of its Cauchy-Green tensor in \(L^{1}\)
• New integral estimates for deformations in terms of their nonlinear strains
• Ordinary differential equations of non-linear elasticity. I: Foundations of the theories of non-linearly elastic rods and shells
• Convexity conditions and existence theorems in nonlinear elasticity
• The continuity of a surface as a function of its two fundamental forms.
• Continuity of a deformation as a function of its Cauchy-Green tensor
• Recovery of a manifold with boundary and its continuity as a function of its metric tensor
• RECOVERY OF A SURFACE WITH BOUNDARY AND ITS CONTINUITY AS A FUNCTION OF ITS TWO FUNDAMENTAL FORMS
• Rotation and strain
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity