#### Abstract

Applications in continuum mechanics often require the energy function
to be nonconvex. In the calculus of variations, different notions of
convexity play an important role. In both cases, few examples of
specific functions are known (since, usually, physical laws impose
additional symmetry conditions). The aim of this talk is to present
some methods to construct such functions in a systematic way.

First, I will discuss nonconvex functions which are invariant under a
discrete symmetry group and depend on the temperature as a
parameter. These functions may serve as energy functions for phase
transitions in crystals. This approach yields a formal description of
all $C^\infty$ potentials.

In the second part, polyconvex frame-indifferent functions are
considered. The aim is to extend Ball's theorem (ARMA '77) on
isotropic polyconvex functions. I present a sufficient condition
describing a large class of frame-indifferent polyconvex functions.

*THURSDAY, December 6, 2001*

**Time:** 3:30 P.M.

**Location:** Physical Plant Building 300