GT Calcul des variations

Mardi 23 octobre 2018 17:15-18:15 - Marc Pegon - Marc Pegon (Université Paris Diderot)

Résumé : Partial Regularity of Stationary $s$-harmonic maps into spheres
In a paper dating back to 1991, L.C. Evans produced a partial regularity result for stationary harmonic maps from $\mathbbR^N$ into spheres. His proof relies on properties of so-called div-curl quantities, i.e. products of divergence-free and curl-free vector fields. Recently, A. Schikorra and C. Mazowiecka introduced fractional div-curl quantities which allows them to derive a new proof of the regularity of 1/2-harmonic maps from $\R$ into a general target manifold. Using their new fractional div-curl estimate it is now possible, following Evans’s original proof in the local case, to establish partial regularity results for stationary $s$-harmonic maps from $\mathbbR^N$ into spheres. In this talk I will introduce the fractional setting, present the ideas of the proof by Evans in the local case, and elaborate on the main adjustments to make it work in this setting.

GT Calcul des variations  Version PDF