On multivortex solutions in Chern-Simons gauge theory

Struwe, Michael ; Tarantello, Gabriella

Bollettino dell'Unione Matematica Italiana, Tome 1-A (1998), p. 109-121 / Harvested from Biblioteca Digitale Italiana di Matematica

Résumé

Motivati dall'analisi asintotica dei vortici nella teoria di Chern-Simons-Higgs, si studia l'equazione $$ - \Delta u= \lambda\left(\frac{e^{u}}{\int_{\Omega}e^{u}\,dx}-\frac{1}{|\Omega|}\right), \quad u\in H^{1}(\Omega) $$ dove $\Omega=\mathbb{R}^{2}/\mathbb{Z}^{2}$ é il toro piatto bidimensionale. In contrasto con l'analogo problema di Dirichlet, si dimostra che per $\lambda\in (8\pi, 4\pi^{2})$ l'equazione ammette una soluzione non banale. Tale soluzione cattura il carattere bidimensionale dell'equazione, nel senso che, per tali valori di $\lambda$, l'equazione non può ammettere soluzioni (periodiche) non banali dipendenti da una sola variabile (vedi [10]).

Détail

Publié le : 1998-02-01

MR 1619043 | Zbl 0912.58046

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