Free Access
Issue
ESAIM: COCV
Volume 16, Number 3, July-September 2010
Page(s) 648 - 676
DOI https://doi.org/10.1051/cocv/2009018
Published online 02 July 2009
  1. P. Antunes and P. Freitas, New bounds for the principal Dirichlet eigenvalue of planar regions. Experiment. Math. 15 (2006) 333–342. [MathSciNet]
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  3. D. Borisov and P. Freitas, Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions on thin planar domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 547–560. [CrossRef] [MathSciNet]
  4. P. Freitas, Upper and lower bounds for the first Dirichlet eigenvalue of a triangle. Proc. Amer. Math. Soc. 134 (2006) 2083–2089. [CrossRef] [MathSciNet]
  5. P. Freitas, Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi. J. Funct. Anal. 251 (2007) 376–398. [CrossRef] [MathSciNet]
  6. J. Hersch, Constraintes rectilignes parallèles et valeurs propres de membranes vibrantes. Z. Angew. Math. Phys. 17 (1966) 457–460. [CrossRef] [MathSciNet]
  7. W. Hooker and M.H. Protter, Bounds for the first eigenvalue of a rhombic membrane. J. Math. Phys. 39 (1960/1961) 18–34.
  8. E. Makai, On the principal frequency of a membrane and the torsional rigidity of a beam, in Studies in mathematical analysis and related topics, Essays in honor of George Pólya, Stanford Univ. Press, Stanford (1962) 227–231.
  9. P.J. Méndez-Hernández, Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius. Duke Math. J. 113 (2002) 93–131. [CrossRef] [MathSciNet]
  10. G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Annals of Mathematical Studies 27. Princeton University Press, Princeton (1951).
  11. M.H. Protter, A lower bound for the fundamental frequency of a convex region. Proc. Amer. Math. Soc. 81 (1981) 65–70. [MathSciNet]
  12. C.K. Qu and R. Wong, “Best possible” upper and lower bounds for the zeros of the Bessel fuction Jv(x). Trans. Amer. Math. Soc. 351 (1999) 2833–2859. [CrossRef] [MathSciNet]
  13. B. Siudeja, Sharp bounds for eigenvalues of triangles. Michigan Math. J. 55 (2007) 243–254. [CrossRef] [MathSciNet]
  14. B. Siudeja, Isoperimetric inequalities for eigenvalues of triangles. Ind. Univ. Math. J. (to appear).

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