Miroslav Silhavy, Mathematical Institute, Academy of Sciences of the Czech Republic, Prague.
"Relaxation in a class of SO(n)--invariant energies related to nematic elastomers"
A class of isotropic energy functions W is determined which admit explicit relaxation. Within the class, the rank 1 convex, quasiconvex, and polyconvex hulls coincide and reduce to the ``Baker--Ericksen hull'' MW, ie, the largest function below W satisfying the Baker--Ericksen inequalities. The construction of MW is based on the monotonicity of SO(n)-invariant rank 1 convex functions and on the classical ordered--forces inequalities for symmetric convex functions. The class includes compressible or incompressible energies of nematic elastomers. The relaxed energy leads to a phase diagram which displays the original solid phase, a liquid phase, and one or two intermediate solid--liquid phases.
THURSDAY, March 14, 2002