Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Isoperimetric inequalities for the first Dirichlet eigenvalue are discussed, with application to the development of an approximate formula appropriate for thin strip domains.


References [Enhancements On Off] (What's this?)

  • [1] L. E. Payne, Isoperimetric inequalities and their applications, SIAM Review 9, 453-488 (1967) MR 0218975
  • [2] L. E. Payne, Isoperimetric inequalities, maximum principles and their applications, Report of lectures given at the University, Newcastle-upon-Tyne (1972)
  • [3] J. W. McLaurin, A general coupled equation approach for solving the biharmonic boundary value problem, SIAM J, Numer. Anal. 11, 14-33 (1974) MR 0349042
  • [4] J. R. Kuttler and V. G. Sigillito, Inequalities for membrane and Stekloff eigenvalues, J. Math. Anal. Appl. 23, 148-160 (1968) MR 0226226
  • [5] L. E. Payne, Some isoperimetric inequalities for harmonic functions, SIAM J. Math. Anal. 1, 354-359 (1970) MR 0437782
  • [6] J. Hersch and L. E. Payne, One-dimensional auxiliary problems and a priori bounds, Abh. Math. Sem. Univ. Hamburg 36, 56-65 (1971) MR 0323132
  • [7] J. R. Kuttler, Remarks on a Stekloff eigenvalue problem, SIAM J. Numer. Anal. 9, 1-5 (1972) MR 0303760
  • [8] 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) MR 0079705
  • [9] 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) MR 0351225
  • [10] S.-L. Fu and L. Wheeler, Stress bounds for bars in torsion, J. Elasticity 3, 1-13 (1973) MR 0475082
  • [11] L. Wheeler and S.-L. Fu, Stress bounds for twisted bars of strip cross section, Int. J. Solids Struct. 10, 461-468 (1974)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35P15

Retrieve articles in all journals with MSC: 35P15


Additional Information

DOI: https://doi.org/10.1090/qam/481624
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society