2 research outputs found
Orlicz-Sobolev nematic elastomers
We extend the existence theorems in Barchiesi et al. (2017), for models of nematic
elastomers and magnetoelasticity, to a larger class in the scale of Orlicz spaces.
These models consider both an elastic term where a polyconvex energy density is
composed with an unknown state variable defined in the deformed configuration,
and a functional corresponding to the nematic energy (or the exchange and
magnetostatic energies in magnetoelasticity) where the energy density is integrated
over the deformed configuration. In order to obtain the desired compactness and
lower semicontinuity, we show that the regularity requirement that maps create
no new surface can still be imposed when the gradients are in an Orlicz class with
an integrability just above the space dimension minus one