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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.

MSC:

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

Citations:

Zbl 0809.35019
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