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

Banff International Research Station for Mathematical Innovation and Discovery

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 (Universit\'e Paris-Est).

Mathematics; Partial differential equations; Integral equations

video/mp4

Author affiliation: Technion-Israel Institute of Technology

2017-10-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63170

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/