The nodal line of the second eigenfunction of the laplacian in IR2 can be closed

Duke Mathematical Journal

Volumn 90, Issue 3, 1997, Pages 631-640

  Hoffmann Ostenhof, M ^a   Hoffmann Ostenhof, T ^b,c   Nadirashvili, N ^d,e  

^a UNIVERSITY OF VIENNA   (Austria)

^b UNIVERSITY OF VIENNA   (Austria)

^c Erwin Schrodinger International Institute for Mathematical Physics   (Austria)

^d International erwln schrödinger institute for mathematical physics   (Australia)

^e Institut for prols of information transmission   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005622808     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-97-09017-7     Document Type: Article

References (10)

1. G. Alessandrini, Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains, Comment. Math. Helv. 69 (1994), 142-154.
2. S. Axler, P. Bourdon, and W. Ramey, Harmonic Function Theory, Grad. Texts in Math. Springer-Verlag, New York, 1992.
3. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss. 224, Springer-Verlag, Berlin, 1983.
4. D. Grieser and D. Jerison, Asymptotics of the first nodal line of a convex domain, Invent. Math. 125 (1996), 197-219.
5. D. Jerison, The diameter of the first nodal line of a convex domain, Ann. of Math. (2) 141 (1995), 1-33.
6. 2, J. Differential Geom. 35 (1992), 255-263.
7. N. S. Nadirashvili, Multiplicity of the eigenvalues of the Neumann problem, Dokl. Akad. Nauk SSSR 286 (1986), 1303-1305.
8. L. E. Payne, Isoperimetric inequalities and their applications, SIAM Rev. 9 (1967), 453-488.
9. P. Stollmann, A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains, Math. Z. 219 (1995), 275-287.
10. S.-T. Yau, “Problem section” in Seminar on Differential Geometry, Ann. of Math. Stud. 102, Princeton Univ. Press, Princeton, 1982, 669-706.