Inequalities for Dirichlet and Neumann eingenvalues of the laplacian for domains on spheres
Journées équations aux dérivées partielles (1997), article no. 1, 15 p. 
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Ashbaugh, M.; Levine, Howard A. Inequalities for Dirichlet and Neumann eingenvalues of the laplacian for domains on spheres. Journées équations aux dérivées partielles (1997), article  no. 1, 15 p. http://archive.numdam.org/item/JEDP_1997____A1_0/

[1] M. Abramowitz and I.A. Stegun, editors, Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series, vol. 55, U.S. Government Printing Office, Washington, D.C., 1964. | MR | Zbl

[2] M.S. Ashbaugh and R.D. Benguria, Universal bounds for the low eigenvalues of Neumann Laplacians in n dimensions, SIAM J. Math. Anal. 24 (1993), 557-570. | MR | Zbl

[3] M.S. Ashbaugh and R.D. Benguria, Isoperimetric inequalities for eigenvalue ratios, Partial Differential Equations of Elliptic Type, Cortona, 1992, A. Alvino, E. Fabes, and G. Talenti, editors, Symposia Mathematica, vol. 35, Cambridge University Press, Cambridge, 1994, pp. 1-36. | MR | Zbl

[4] M.S. Ashbaugh and R.D. Benguria, Sharp upper bound to the first nonzero Neumann eigenvalue for bounded domains in spaces of constant curvature, J. London Math. Soc. (2) 52 (1995), 402-416. | MR | Zbl

[5] P. Aviles, Symmetry theorems related to Pompeiu's problem, Amer. J. Math. 108 (1986), 1023-1036. | MR | Zbl

[6] C. Bandle, Isoperimetric Inequalities and Applications, Pitman Monographs and Studies in Mathematics, vol. 7, Pitman, Boston, 1980. | MR | Zbl

[7] I. Chavel, Lowest eigenvalue inequalities, Proc. Symp. Pure Math., vol. 36, Geometry of the Laplace Operator, R. Osserman and A. Weinstein, editors, Amer. Math. Soc., Providence, R.I., 1980, pp. 79-89. | MR | Zbl

[8] I. Chavel, Eigenvalues in Riemannian Geometry, Academic, New York, 1984. | MR | Zbl

[9] G. Faber, Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt, Sitzungberichte der mathematisch-physikalischen Klasse der Bayerischen Akademie der Wissenschaften zu München Jahrgang, 1923, pp. 169-172. | JFM

[10] S. Friedland and W.K. Hayman, Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions, Comment. Math. Helvetici 51 (1976), 133-161. | MR | Zbl

[11] L. Friedlander, Some inequalities between Dirichlet and Neumann eigenvalues, Arch. Rational Mech. Anal. 116 (1991), 153-160. | MR | Zbl

[12] E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises, Math. Ann. 94 (1925), 97-100. | JFM

[13] E. Krahn, Über Minimaleigenschaften der Kugel in drei und mehr Dimensionen, Acta Comm. Univ. Tartu (Dorpat) A9 (1926), 1-44 [English translation in Edgar Krahn 1894-1961: A Centenary Volume, Ü. Lumiste and J. Peetre, editors, IOS Press, Amsterdam, 1994, pp. 139-174]. | JFM

[14] H.A. Levine, Some remarks on inequalities between Dirichlet and Neumann eigenvalues, Maximum Principles and Eigenvalue Problems in Partial Differential Equations, P.W. Schaefer, editor, Pitman Research Notes in Mathematics Series, vol. 175, Longman Scientific and Technical, Harlow, Essex, United Kingdom, 1988, pp. 121-133. | MR | Zbl

[15] H.A. Levine and H.F. Weinberger, Inequalities between Dirichlet and Neumann eigenvalues, Arch. Rational Mech. Anal. 94 (1986), 193-208. | MR | Zbl

[16] R. Mazzeo, Remarks on a paper of Friedlander concerning inequalities between Neumann and Dirichlet eigenvalues, Int. Math. Research Notices, No. 4 (1991), 41-48. | MR | Zbl

[17] R. Molzon, Symmetry and overdetermined boundary value problems, Forum Math. 3 (1991), 143-156. | MR | Zbl

[18] L.E. Payne, Inequalities for eigenvalues of membranes and plates, J. Rational Mech. Anal. 4 (1955), 517-529. | MR | Zbl

[19] L.E. Payne, Some comments on the past fifty years of isoperimetric inequalities, Inequalities: Fifty Years On from Hardy, Littlewood, and Pólya, W.N. Everitt, editor, Marcel Dekker, New York, 1991, pp. 143-161. | MR | Zbl

[20] F. Rellich, Darstellung der Eigenwerte Δu + λu = 0 durch ein Randintegral, Math. Z. 46 (1940), 635-636. | JFM | MR | Zbl

[21] G.V. Rozenblum, M.A. Shubin, and M.Z. Solomyak, Spectral Theory of Differential Operators (translated from the Russian by T. Zastawniak), Partial Differential Equations VII, M.A. Shubin, editor, Encyclopedia of Mathematical Sciences, vol. 64, R.V. Gamkrelidze, editor-in-chief, Springer, Berlin, 1994. | Zbl

[22] E. Sperner, Zur Symmetrisierung von Funktionen auf Sphären, Math. Z. 134 (1973), 317-327. | MR | Zbl

[23] G. Szegö, Inequalities for certain eigenvalues of a membrane of given area, J. Rational Mech. Anal. 3 (1954), 343-356. | MR | Zbl

[24] H.F. Weinberger, An isoperimetric inequality for the n-dimensional free membrane problem, J. Rational Mech. Anal. 5 (1956), 633-636. | MR | Zbl