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MiS Preprint
19/2007

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

Stefan Müller and Mariapia Palombaro

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.

Received:
Feb 21, 2007
Published:
Feb 21, 2007
MSC Codes:
74N05, 58A25, 74B20, 49J45, 46E40
Keywords:
Crystals, dislocations, currents, nonlinear elasticity

Related publications

inJournal
2008 Journal Open Access
Stefan Müller and Mariapia Palombaro

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

In: Calculus of variations and partial differential equations, 31 (2008) 4, pp. 473-482