报告题目：Polyconvexity and existence theory in nonlinear elasticity
In nonlinear elasticity, the deformation of a body subjected to applied forces can be found by solving a minimization problem. The functional whose minimum is to be found represents the total energy associated with any admissible deformation of the body and is necessarily non-convex. Thus establishing the existence of a minimizer for such a functional cannot rely on classical methods in Calculus of Variations. It relies instead on a weaker notion of convexity, called polyconvexity, which was introduced by J. Ball in a landmark paper in 1977. In this talk, I will give a brief presentation of Ball's theory and then will discuss recent advances in extending this theory from three-dimensional elasticity to two-dimensional shell theory.