An application of a new coercive inequality to variational problems studied in general relativity and in Cosserat elasticity giving the smoothness of minimizers

DOI10.1007/s00013-009-0067-7zbMath1180.49040OpenAlexW2053273806MaRDI QIDQ1047903

Oliver D. Schirra, Fuchs, Martin

Publication date: 8 January 2010

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-009-0067-7

zbMATH Keywords

regularity of minimizersgeneralized Korn's inequality

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Variational principles of physics (49S05) Equations linearized about a deformed state (small deformations superposed on large) (74B15)

Related Items (12)

L^p-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions ⋮ Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions ⋮ Generalizations of Korn's inequality based on gradient estimates in Orlicz spaces and applications to variational problems in 2D involving the trace free part of the symmetric gradient ⋮ New Korn-type inequalities and regularity of solutions to linear elliptic systems and anisotropic variational problems involving the trace-free part of the symmetric gradient ⋮ Poincaré meets Korn via Maxwell: extending Korn's first inequality to incompatible tensor fields ⋮ \(L^p\)-trace-free version of the generalized Korn inequality for incompatible tensor fields in arbitrary dimensions ⋮ Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions ⋮ Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy ⋮ Complexes from complexes ⋮ \(\mathscr{A}\)-quasiconvexity and partial regularity ⋮ An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions ⋮ Trace-Free Korn Inequalities in Orlicz Spaces

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• A numerical study for linear isotropic Cosserat elasticity with conformally invariant curvature

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