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

Details Korn's second inequality and geometric rigidity with mixed growth conditions Korn's second inequality and geometric rigidity with mixed growth conditions

2012-03-06

arxiv.org/abs/1203.1138v1

Mathematics

Analysis of PDEs

Scientific paper

Geometric rigidity states that a gradient field which is $L^p$-close to the set of proper rotations is necessarily $L^p$-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 $L^p+L^q$ and in $L^{p,q}$ interpolation spaces. As a first step we prove the corresponding linear inequality, which generalizes Korn's inequality to these spaces.

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