A variational problem involving a polyconvex integrand

Abstract

Existence of solutions to systems of parabolic equations obtained from polyconvex functions, remains a challenge in PDEs. In the current notes, we keep our focus on a variational problem which originates from a discretization of such a system. We state a duality result for a functional whose integrand is polyconvex and fails to satisfy growth conditions imposed in the standard theory of the calculus of variations.

The current notes are based on a work with Roméo Awi [3] and on a lecture we gave at the meeting “Variatonal Methods for Evolving Objects”, July 30–August 03, 2012, Sapporo, Japan. We express our gratitude to the organizers of the meeting for their support and generous invitation.