Geodesic
On multivortex solutions in Chern-Simons gauge theory
Bollettino della Unione matematica italiana, Série 8, 1B (1998) no. 1, pp. 109-121.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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]). 
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Struwe, Michael; Tarantello, Gabriella. On multivortex solutions in Chern-Simons gauge theory. Bollettino della Unione matematica italiana, Série 8, 1B (1998) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/BUMI_1998_8_1B_1_a5/

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