Some Poincaré-type inequalities for functions of bounded deformation involving the deviatoric part of the symmetric gradient

DOI10.1007/s10958-011-0554-9zbMath1305.74038OpenAlexW2053478949WikidataQ110086268 ScholiaQ110086268MaRDI QIDQ476672

Fuchs, Martin, Sergey I. Repin

Publication date: 2 December 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-011-0554-9

Mathematics Subject Classification ID

Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Regularity of solutions of equilibrium problems in solid mechanics (74G40) Inequalities involving derivatives and differential and integral operators (26D10) PDEs in connection with mechanics of deformable solids (35Q74) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (3)

L^p-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions ⋮ Symmetric-convex functionals of linear growth ⋮ Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy

Cites Work

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• Functions of bounded deformation
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• A priori estimates for differential operators in \(L_ \infty\) norm
• Generalized Korn's inequality and conformal Killing vectors
• An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions
• Two-dimensional variational problems of the theory of plasticity
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