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

Stefan Müller and Mariapia Palombaro

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Submission date: 21. Feb. 2007
Pages: 12
published in: Calculus of variations and partial differential equations, 31 (2008) 4, p. 473-482 
DOI number (of the published article): 10.1007/s00526-007-0120-y
Bibtex
MSC-Numbers: 74N05, 58A25, 74B20, 49J45, 46E40
Keywords and phrases: Crystals, dislocations, currents, nonlinear elasticity
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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 . Thus one needs to consider elastic energies with slow growth, to which the original results of Ball cannot be applied directly.