"On the regularity of minimizers of multiple integrals"

Dr. J. Kristensen (University of Oxford)


We show that the singular set of a Lipschitzian minimizer of a quasiconvex integral is uniformly porous. As a consequence we derive an upper bound for its Hausdorff dimension. The proof of porosity is based on a Carleson type estimate for the excess. In turn, this estimate is a consequence of a Caccioppoli inequality and general properties of Sobolev maps. Finally, we discuss the situation for minimizers of general convex integral functionals, where different methods apply. The talk is based on joint work with Giuseppe Mingione (Parma).