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The first eigenvalue of the Laplacian for plane domains. (English) Zbl 0462.35071

35P15 Estimates of eigenvalues in context of PDEs
52A40 Inequalities and extremum problems involving convexity in convex geometry
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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[1] Jeff Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in analysis (Papers dedicated to Salomon Bochner, 1969) Princeton Univ. Press, Princeton, N. J., 1970, pp. 195 – 199.
[2] S.-Y. Cheng, On the Hayman-Osserman-Taylor inequality (preprint).
[3] W. K. Hayman, Some bounds for principal frequency, Applicable Anal. 7 (1977/78), no. 3, 247 – 254. · Zbl 0383.35053
[4] Robert Osserman, A note on Hayman’s theorem on the bass note of a drum, Comment. Math. Helv. 52 (1977), no. 4, 545 – 555. · Zbl 0374.52008
[5] L. A. Santaló, Sobre el circulo de radio maximo contenido en un recinto, Rev. Un. Mat. Argentina 10 (1945), 155-167.
[6] Michael E. Taylor, Estimate on the fundamental frequency of a drum, Duke Math. J. 46 (1979), no. 2, 447 – 453. · Zbl 0418.35068
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