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Annali di Matematica Pura ed Applicata

, Volume 192, Issue 5, pp 815–851 | Cite as

Symmetric tensor fields of bounded deformation

  • Kristian BrediesEmail author
Article

Abstract

We introduce and study spaces of symmetric tensor fields of bounded deformation for tensors of arbitrary order, i.e., where the symmetrized derivative is still a Radon measure. A Sobolev–Korn type estimate, a boundary trace theorem and continuous as well as compact embedding properties into Lebesgue spaces are obtained, showing that these spaces can be regarded as a natural generalization of the spaces of bounded deformation to higher-order symmetric tensors.

Keywords

Symmetric tensor fields Bounded deformation Sobolev–Korn inequality Boundary traces Continuous/compact embeddings 

Mathematics Subject Classification (2000)

46E35 53A45 74B20 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute of Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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