Isoperimetric inequalities for the Dirichlet eigenvalue problem
Authors:
Cornelius O. Horgan and Lewis T. Wheeler
Journal:
Quart. Appl. Math. 35 (1977), 406-409
MSC:
Primary 35P15
DOI:
https://doi.org/10.1090/qam/481624
MathSciNet review:
481624
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Abstract: Isoperimetric inequalities for the first Dirichlet eigenvalue are discussed, with application to the development of an approximate formula appropriate for thin strip domains.
- L. E. Payne, Isoperimetric inequalities and their applications, SIAM Rev. 9 (1967), 453–488. MR 218975, DOI https://doi.org/10.1137/1009070
L. E. Payne, Isoperimetric inequalities, maximum principles and their applications, Report of lectures given at the University, Newcastle-upon-Tyne (1972)
- Johnnie William McLaurin, A general coupled equation approach for solving the biharmonic boundary value problem, SIAM J. Numer. Anal. 11 (1974), 14–33. MR 349042, DOI https://doi.org/10.1137/0711003
- J. R. Kuttler and V. G. Sigillito, Inequalities for membrane and Stekloff eigenvalues, J. Math. Anal. Appl. 23 (1968), 148–160. MR 226226, DOI https://doi.org/10.1016/0022-247X%2868%2990123-6
- L. E. Payne, Some isoperimetric inequalities for harmonic functions, SIAM J. Math. Anal. 1 (1970), 354–359. MR 437782, DOI https://doi.org/10.1137/0501032
- Joseph Hersch and Lawrence E. Payne, One-dimensional auxillary problems and a priori bounds, Abh. Math. Sem. Univ. Hamburg 36 (1971), 57–65. MR 323132, DOI https://doi.org/10.1007/BF02995908
- James R. Kuttler, Remarks on a Stekloff eigenvalue problem, SIAM J. Numer. Anal. 9 (1972), 1–5. MR 303760, DOI https://doi.org/10.1137/0709001
- Gaetano Fichera, Su un principio di dualità per talune formole di maggiorazione relative alle equazioni differenziali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 19 (1955), 411–418 (1956) (Italian). MR 79705
- L. E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. Math. Special Issue Special Issue (1968/69), part I, 51–59. Special issue presented to Professor Bibhutibhusan Sen on the occasion of his seventieth birthday, Part I. MR 0351225
- Shein Liang Fu and Lewis Wheeler, Stress bounds for bars in torsion, J. Elasticity 3 (1973), no. 1, 1–13 (English, with German summary). MR 475082, DOI https://doi.org/10.1007/BF00045793
L. Wheeler and S.-L. Fu, Stress bounds for twisted bars of strip cross section, Int. J. Solids Struct. 10, 461–468 (1974)
L. E. Payne, Isoperimetric inequalities and their applications, SIAM Review 9, 453–488 (1967)
L. E. Payne, Isoperimetric inequalities, maximum principles and their applications, Report of lectures given at the University, Newcastle-upon-Tyne (1972)
J. W. McLaurin, A general coupled equation approach for solving the biharmonic boundary value problem, SIAM J, Numer. Anal. 11, 14–33 (1974)
J. R. Kuttler and V. G. Sigillito, Inequalities for membrane and Stekloff eigenvalues, J. Math. Anal. Appl. 23, 148–160 (1968)
L. E. Payne, Some isoperimetric inequalities for harmonic functions, SIAM J. Math. Anal. 1, 354–359 (1970)
J. Hersch and L. E. Payne, One-dimensional auxiliary problems and a priori bounds, Abh. Math. Sem. Univ. Hamburg 36, 56–65 (1971)
J. R. Kuttler, Remarks on a Stekloff eigenvalue problem, SIAM J. Numer. Anal. 9, 1–5 (1972)
G. Fichera, Su un principio di dualità per talune formole maggiorazione relative alle equazioni differenziali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 19, 411–418 (1955)
L. E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem, Indian J. Mech. Math., special issue in honor of B. Sen, Part I, 51–59 (1968)
S.-L. Fu and L. Wheeler, Stress bounds for bars in torsion, J. Elasticity 3, 1–13 (1973)
L. Wheeler and S.-L. Fu, Stress bounds for twisted bars of strip cross section, Int. J. Solids Struct. 10, 461–468 (1974)
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Article copyright:
© Copyright 1977
American Mathematical Society