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MR1480548 (98m:35146) 35P15 (35J05)
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Nadirashvili, N. The nodal line of the second eigenfunction of the Laplacian in $R\sp 2$ can be closed. Duke Math. J. 90 (1997), no. 3, 631--640.
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