Korn’s second inequality and geometric rigidity with mixed growth conditions

By Sergio Conti, Georg Dolzmann, Stefan Müller. 2012

55 citations recorded by the source corpus.

Geometric rigidity states that a gradient field which is $$L^p$$Lp-close to the set of proper rotations is necessarily $$L^p$$Lp-close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in the theory of plasticity, energy densities with mixed growth appear. We show here that geometric rigidity holds also in $$L^p+L^q$$Lp+Lq and in $$L^{p,q}$$Lp,q interpolation spaces. As a first step we prove the corresponding linear inequality, which generalizes Korn’s inequality to these spaces.

Subfields: Applied Mathematics, Biomedical Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/99eef306cb4d57b746f8e4e31a60f7518cf7f11c

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In Applied Mathematics

In Biomedical Engineering

In Materials Chemistry

Citations in the corpus

Korn-Poincaré inequalities for functions with a small jump set (2016, background): “This has been generalized to many different settings, including the geometrically nonlinear case [FJM02], mixed growth [CDM14] and incompatible strain fields which contain dislocations [NPW12, MSZ14].”