Orateur
Description
Over 30 years ago Frédéric Hélein proved that all harmonic maps from surfaces into compact Riemannian manifolds are smooth. Despite the existence of several partial results, for $n>2$ the counterpart of this theorem is wide open. In a recent work with two coauthors, Michał Miśkiewicz and Bogdan Petraszczuk, we prove regularity of $n$-harmonic maps into compact Riemannian manifolds and weak solutions to $H$-systems in dimension $n$, under an extra assumption: that $n/2$-th derivatives of the solution are square integrable. The tools used in the proof involve, as one might guess, Hardy spaces and BMO, and the Rivière--Uhlenbeck decomposition (with estimates in Morrey spaces). A particularly prominent role is played by the Coifman--Rochberg--Weiss commutator theorem.
