Finite Potential Energy for Entire Solutions of the Planar Ginzburg--Landau Equation

Hongge Chen, Juncheng Wei, Haicheng Yan +1

We prove that every smooth entire solution $u:{\mathbb{R}}^2\to {\mathbb{R}}^2$ of the Ginzburg--Landau equation $-\Delta u=u(1-|u{|}^2)$ with $|u(x)|\to 1$ as $|x|\to \infty$ has fi…