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Séminaire EDP-Analyse ICJ

Small energy Ginzburg-Landau minimizers in ${\mathbb R}^3$

by Itaï Shafrir (Technion - Israel Institute of Technology)

mardi 30 mai 2017 de au (Europe/Paris)
at Université Claude Bernard Lyon 1 - Campus de la Doua, Bâtiment Braconnier ( Fokko Du Cloux )
Description
We study global solutions $u:{\mathbb R}^3\to{\mathbb R}^2$ of the Ginzburg-Landau equation $-\Delta u=(1-|u|^2)u$ which are local minimizers in the sense of De Giorgi.
We prove that a local minimizer satisfying the condition $\liminf_{R\to\infty}\frac{E(u;B_R)}{R\ln R}<2\pi$ must be constant. The main tool is a new sharp $\eta$-ellipticity result for minimizers in dimension three that might be of independent interest.
This is a joint work with Etienne Sandier (Université Paris-Est).