Counterexamples to Korn’s inequality with non-constant rotation coefficients

DOI10.1177/1081286510367554zbMath1269.74017OpenAlexW2003653216WikidataQ124821721 ScholiaQ124821721MaRDI QIDQ2842386

Waldemar Pompe

Publication date: 14 August 2013

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1081286510367554

zbMATH Keywords

Korn's inequalitycoercive inequalities

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (7)

Unique continuation for first-order systems with integrable coefficients and applications to elasticity and plasticity ⋮ Counterexamples in the theory of coerciveness for linear elliptic systems related to generalizations of Korn's second inequality ⋮ Uniqueness of integrable solutions to \(\nabla\zeta=G\zeta\), \(\zeta|_\Gamma=0\) for integrable tensor coefficients \(G\) and applications to elasticity ⋮ The isotropic Cosserat shell model including terms up to \(O(h^5)\). II: Existence of minimizers ⋮ Surface couplings for subdomain-wise isoviscous gradient based Stokes finite element discretizations ⋮ Poincaré meets Korn via Maxwell: extending Korn's first inequality to incompatible tensor fields ⋮ Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions

Cites Work

• Unnamed Item
• Symmetric Cauchy stresses do not imply symmetric Biot strains in weak formulations of isotropic hyperelasticity with rotational degrees of freedom
• Implicit partial differential equations
• A geometrically exact Cosserat shell model for defective elastic crystals. Justification via \(\Gamma\)-convergence
• Existence of minimizers for a geometrically exact Cosserat solid
• Local existence and uniqueness for a geometrically exact membrane-plate with viscoelastic transverse shear resistance
• Existence of minimizers for a finite-strain micromorphic elastic solid
• On Korn's first inequality with non-constant coefficients
• A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS
• Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation
• ON COERCIVITY IN NONISOTROPIC SOBOLEV SPACES

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