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solenoidal fields

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Attainment results for nematic elastomers
Part of
Virginia Agostiniani, Gianni Dal Maso, Antonio DeSimone
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 145 / Issue 4 / August 2015

Published online by Cambridge University Press:

08 July 2015, pp. 669-701

Print publication:

August 2015
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We consider a class of non-quasi-convex frame indifferent energy densities that includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem, we provide an explicit minimizer of the energy functional satisfying a non-trivial boundary condition. Other attainment results, both for the nonlinear and the linearised model, are obtained by using the theory of convex integration introduced by Müller and Šverák in the context of crystalline solids.