Séminaire EDP-Analyse ICJ

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

## by Itaï Shafrir (Technion - Israel Institute of Technology)

Europe/Paris
Fokko Du Cloux (Université Claude Bernard Lyon 1 - Campus de la Doua, Bâtiment Braconnier)

### Fokko Du Cloux

#### Université Claude Bernard Lyon 1 - Campus de la Doua, Bâtiment Braconnier

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).
###### Your browser is out of date!

Update your browser to view this website correctly. Update my browser now

×