Local minimizers for the Ginzburg-Landau equation are radially symmetric. (Les minimiseurs locaux pour l’équation de Ginzburg-Landau sont à symétrie radiale.) (French. Abridged English version) Zbl 0858.35038

Summary: We consider the equation \(-\Delta u=u(1-|u|^2)\) in \(\mathbb{R}^2\). We prove that local minimizers (in the sense of H. Brezis, F. Merle and T. Rivière [Arch. Ration. Mech. Anal. 126, No. 1, 135-158 (1994; Zbl 0809.35019)]) are radial. We find sufficient conditions for the radial symmetry of other solutions.


35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs


Zbl 0809.35019