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

MSC:
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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References:
[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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