Sharp bounds for eigenvalues of triangles

Michigan Mathematical Journal

Volumn 55, Issue 2, 2007, Pages 243-254

  Siudeja, BartŁomiej ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36249023260     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1187646992     Document Type: Review

References (9)

1. P. Antunes and P. Freitas, New bounds for the principal Dirichlet eigenvalue of planar regions, Experiment. Math. 15 (2006), 333-342.
2. P. Freitas, Upper and lower bounds for the first Dirichlet eigenvalue of a triangle, Proc. Amer. Math. Soc. 134 (2006), 2083-2089 (electronic).
3. E. Makai, On the principal frequency of a membrane and the torsion rigidity of a beam, Studies in mathematical analysis and related topics: Essays in honor of George Pólya, pp. 227-231, Stanford Univ. Press, Stanford, CA, 1962.
4. B. McCartin, Eigenstructure of the equilateral triangle. I. The Dirichlet problem, SIAM Rev. 45 (2003), 267-287.
5. R. Osserman, A note on Hayman's theorem on the bass note of a drum, Comment. Math. Helv. 52 (1977), 545-555.
6. M. A. Pinsky, The eigenvalues of an equilateral triangle, SIAM J. Math. Anal. 11 (1980), 819-827.
7. G. Pólya, Two more inequalities between physical and geometrical quantities, J. Indian Math. Soc. (N.S.) 24 (1960), 413-419.
8. G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Ann. of Math. Stud., 27, Princeton Univ. Press, Princeton, NJ, 1951.
9. v(x), Trans. Amer. Math. Soc. 351 (1999), 2833-2859.