The nodal line of the second eigenfunction of the Laplacian in $\mathbb{R}^2$ can be closed
M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and N. Nadirashvili
Source: Duke Math. J. Volume 90, Number 3
(1997), 631-640.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077232816
Mathematical Reviews number (MathSciNet): MR1480548
Zentralblatt MATH identifier: 0956.35027
Digital Object Identifier: doi:10.1215/S0012-7094-97-09017-7
References
[A] G. Alessandrini, Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains, Comment. Math. Helv. 69 (1994), no. 1, 142–154.
Mathematical Reviews (MathSciNet): MR95d:35111
Zentralblatt MATH: 0838.35006
Digital Object Identifier: doi:10.1007/BF02564478
[ABR] S. Axler, P. Bourdon, and W. Ramey, Harmonic function theory, Graduate Texts in Mathematics, vol. 137, Springer-Verlag, New York, 1992.
Mathematical Reviews (MathSciNet): MR93f:31001
Zentralblatt MATH: 0765.31001
[GT] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR86c:35035
Zentralblatt MATH: 0562.35001
[GJ] D. Grieser and D. Jerison, Asymptotics of the first nodal line of a convex domain, Invent. Math. 125 (1996), no. 2, 197–219.
Mathematical Reviews (MathSciNet): MR97d:35033
Zentralblatt MATH: 0857.31002
Digital Object Identifier: doi:10.1007/s002220050073
[J] D. Jerison, The diameter of the first nodal line of a convex domain, Ann. of Math. (2) 141 (1995), no. 1, 1–33.
Mathematical Reviews (MathSciNet): MR95k:35148
Zentralblatt MATH: 0831.35115
Digital Object Identifier: doi:10.2307/2118626
[M] A. D. Melas, On the nodal line of the second eigenfunction of the Laplacian in $\bf R\sp 2$, J. Differential Geom. 35 (1992), no. 1, 255–263.
Mathematical Reviews (MathSciNet): MR93g:35100
Zentralblatt MATH: 0769.58056
Project Euclid: euclid.jdg/1214447811
[N] N. S. Nadirashvili, Multiplicity of eigenvalues of the Neumann problem, Dokl. Akad. Nauk SSSR 286 (1986), no. 6, 1303–1305.
Mathematical Reviews (MathSciNet): MR88a:35068
Zentralblatt MATH: 0613.35052
[P] L. E. Payne, Isoperimetric inequalities and their applications, SIAM Rev. 9 (1967), 453–488.
Mathematical Reviews (MathSciNet): MR36:2058
Zentralblatt MATH: 0154.12602
Digital Object Identifier: doi:10.1137/1009070
JSTOR: links.jstor.org
[S] P. Stollmann, A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains, Math. Z. 219 (1995), no. 2, 275–287.
Mathematical Reviews (MathSciNet): MR96d:60119
Zentralblatt MATH: 0822.31005
Digital Object Identifier: doi:10.1007/BF02572365
[Y] S.-T. Yau, Problem section, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 669–706.
Mathematical Reviews (MathSciNet): MR83e:53029
Zentralblatt MATH: 0479.53001
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