Calculus of Variations and Geometric Measure Theory

V. Agostiniani - G. Dal Maso - A. DeSimone

Attainment results for nematic elastomers

created by dalmaso on 22 Oct 2013
modified on 18 Nov 2015


Published Paper

Inserted: 22 oct 2013
Last Updated: 18 nov 2015

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Volume: 145
Pages: 669-701
Year: 2015
Doi: 10.1017/S0308210515000128


We consider a class of non-quasiconvex frame indifferent energy densities which 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 nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.