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Über Knoten von Eigenfunktionen des Laplace-Beltrami-Operators. (German) Zbl 0349.58012

MSC:
58J99 Partial differential equations on manifolds; differential operators
35P05 General topics in linear spectral theory for PDEs
47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX)
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References:
[1] Agmon, S.: Lectures on elliptic boundary value problems. Princeton: Van Nostrand 1965 · Zbl 0142.37401
[2] Albert, J.H.: Nodal and critical sets for eigenfunctions of elliptic operators. In: Proceedings of Symposia in Pure Mathematics. Vol. 28. Partial Differential Equations (Berkeley 1971) pp. 71-78. Providence: American Mathematical Society 1973
[3] Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. pur. appl. IX. Sér.36, 235-249 (1957) · Zbl 0084.30402
[4] Berger, M., Gauduchon, P., Mazet, E.: Le spectre d’une variété Riemannienne. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0223.53034
[5] Brüning, J., Gromes, D. Über die Länge der Knotenlinien schwingender Membranen. Math. Z.124, 79-82 (1972) · Zbl 0226.35078 · doi:10.1007/BF01142586
[6] Cheeger, J., Ebin, D.: Comparison theorems in Riemannian geometry. Amsterdam, Oxford: North-Holland 1975 · Zbl 0309.53035
[7] Cheng, S.-Y.: Eigenfunctions and nodal sets. Commentarii math. Helvet.51, 43-55 (1976) · Zbl 0334.35022 · doi:10.1007/BF02568142
[8] Courant, R., Hilbert, D.: Methoden der mathematischen Physik I. Berlin: Springer 1930 · Zbl 0156.23201
[9] Krahn, E.: Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises. Math. Ann.94, 97-100 (1925) · JFM 51.0356.05 · doi:10.1007/BF01208645
[10] Peetre, J.: A generalization of Courant’s nodal domain theorem. Math. Scandinav.5, 15-20 (1957) · Zbl 0077.30101
[11] Pleijel, Å.: Remarks on Courant’s nodal line theorem. Commun. pure appl. Math.9, 543-550 (1956) · Zbl 0070.32604 · doi:10.1002/cpa.3160090324
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