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Marc Pégon
Lundi 5 novembre 2018
Marc Pégon (Université Paris Diderot)
Partial Regularity of Stationary $s$-harmonic maps into spheres.
Résumé :
In a paper dating back to 1991, L.C. Evans produced a partial regularity result for stationary harmonic maps from \R^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 \R^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.