A Remark on Polyconvex Functions with Symmetry

For a given polyconvex function W , among all associated convex functions g of minors there exists the largest one; this function inherits all symmetry properties of W . For a given associated (not necessarily the largest) function g , one can still find an associated (possibly not the largest) function with the symmetry of W . This function is constructed by averaging of symmetry conjugated functions over the symmetry group of W using Haar’s measure. It follows that if a symmetric polyconvex function W has class k =0,…,∞ associated function, then the averaging produces a symmetric associated function that is class k as well.