Calculus of Variations

The questions of existence and regularity for minimizers of variational integrals lead in the vectorial multi-dimensional case to the introduction of various notions of convexity, notably rank-one convexity, quasiconvexity and polyconvexity.

While not apparent at the outset these notions turn out to play a role in a much wider context, and appear for instance naturally in the study of PDEs when the so-called weak convergence methods are applied and also in many fundamental problems that involve integral estimates of derivatives of mappings.

Faculty: John BallJan Kristensen and Luc Nguyen

DPhil students: Cristiana de Filippis, Andre Guerra and Adam Prosinski