A lower bound for the fundamental frequency of a convex region
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- by M. H. Protter PDF
- Proc. Amer. Math. Soc. 81 (1981), 65-70 Request permission
Abstract:
A lower bound for the first eigenvalue of the Laplace operator is obtained in terms of the radius of the largest ball which can be inscribed in a convex region in ${R^n}$, $n \geqslant 2$.References
- W. K. Hayman, Some bounds for principal frequency, Applicable Anal. 7 (1977/78), no. 3, 247–254. MR 492339, DOI 10.1080/00036817808839195
- Joseph Hersch, Sur la fréquence fondamentale d’une membrane vibrante: évaluations par défaut et principe de maximum, Z. Angew. Math. Phys. 11 (1960), 387–413 (French, with English summary). MR 125319, DOI 10.1007/BF01604498
- Robert Osserman, A note on Hayman’s theorem on the bass note of a drum, Comment. Math. Helv. 52 (1977), no. 4, 545–555. MR 459099, DOI 10.1007/BF02567388
- Robert Osserman, Bonnesen-style isoperimetric inequalities, Amer. Math. Monthly 86 (1979), no. 1, 1–29. MR 519520, DOI 10.2307/2320297
- L. E. Payne and I. Stakgold, On the mean value of the fundamental mode in the fixed membrane problem, Applicable Anal. 3 (1973), 295–306. MR 399633, DOI 10.1080/00036817308839071
- M. H. Protter, Lower bounds for the first eigenvalue of elliptic equations, Ann. of Math. (2) 71 (1960), 423–444. MR 111923, DOI 10.2307/1969937
- Michael E. Taylor, Estimate on the fundamental frequency of a drum, Duke Math. J. 46 (1979), no. 2, 447–453. MR 534061
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 65-70
- MSC: Primary 35P15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589137-2
- MathSciNet review: 589137