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Existence of minimizers for a polyconvex energy in a crystal with dislocations
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  • Published: 13 July 2007

Existence of minimizers for a polyconvex energy in a crystal with dislocations

  • Stefan Müller1 &
  • Mariapia Palombaro1 

Calculus of Variations and Partial Differential Equations volume 31, pages 473–482 (2008)Cite this article

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Abstract

We provide existence theorems in nonlinear elasticity for minimum problems modeling the deformations of a crystal with a given dislocation. A key technical difficulty is that due to the presence of a the dislocation the elastic deformation gradient cannot be in L 2. Thus one needs to consider elastic energies with slow growth, to which the original results of Ball cannot be applied directly.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, 04103, Leipzig, Germany

    Stefan Müller & Mariapia Palombaro

Authors
  1. Stefan Müller
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  2. Mariapia Palombaro
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Correspondence to Stefan Müller.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Müller, S., Palombaro, M. Existence of minimizers for a polyconvex energy in a crystal with dislocations. Calc. Var. 31, 473–482 (2008). https://doi.org/10.1007/s00526-007-0120-y

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  • Received: 25 February 2007

  • Accepted: 18 May 2007

  • Published: 13 July 2007

  • Issue Date: April 2008

  • DOI: https://doi.org/10.1007/s00526-007-0120-y

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Mathematics Subject Classification (2000)

  • 74N05
  • 58A25
  • 74B20
  • 49J45
  • 46E40
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