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Sur la frequence fondamentale d’une membrane vibrante: evaluations par defaut et principe de maximum. (French) Zbl 0104.41403

Z. Angew. Math. Phys. 11, 387-413 (1960); addendum ibid. 11, 545 (1960).

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[1] R. Courant etD. Hilbert,Methoden der mathematischen Physik, Vol. I (Springer, Berlin 1931). · Zbl 0001.00501
[2] J. Hersch,Une interprétation du principe de Thomson et son analogue pour la fréquence fondamentale d’une membrane. Application. C. R. Acad. Sci. Paris248, 2060 (1959). · Zbl 0085.19302
[3] J. Hersch,Un principe de maximum pour la fréquence fondamentale d’une membrane. C. R. Acad. Sci. Paris249, 1074 (1959). · Zbl 0087.18902
[4] J. Hersch,Sur quelques principes extrémaux de la physique mathématique. (Leçon inaugurale à I’E.P.F.) “L’Enseignement Mathématique{”, 2e série,5, 249–257 (1959).}
[5] W. Hooker etM. H. Protter,Bounds for the first eigenvalue of a rhombic membrane. Tech. Report No. 3, AFOSR Univ. of California, Berkeley (1959). · Zbl 0097.30504
[6] L. E. Payne etH. F. Weinberger,Lower bounds for vibration frequencies of elastically supported membranes and plates. J. Soc. Indust. Appl. Math.5, 171–182 (1957). · Zbl 0083.19406 · doi:10.1137/0105012
[7] G. Pólya etM. Schiffer,Convexity of functionals by transplantation. J. d’Anal. Math.3, 2e partie, 245–345, Jérusalem (1953/54). · Zbl 0056.32701 · doi:10.1007/BF02803593
[8] G. Pólya etG. Szegö,Isoperimetric inequalities in mathematical physics. Princeton University Press (1951).
[9] M. H. Protter,Lower bounds for the first eigenvalue of elliptic equations and related topics. Tech. Report No. 8, AFOSR, Univ. of California, Berkeley (1958). · Zbl 0083.08901
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