Skip to main content
Log in

On the torsion function, Green's function and conformal radius: An isoperimetric inequality of Pólya and Szegö, some extensions and applications

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. C. Bandle,Isoperimetric Inequalities and Applications, Pitman, to appear.

  2. J. Barta,Sur la vibration fondamentale d'une membrane, C. R. Acad. Sci. Paris204 (1937), 472.

    Google Scholar 

  3. P. R. Garabedian,Partial Differential Equations, Wiley, 1964.

  4. J. Hadamard,Mémoire sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées, Mémoires savants étrangers, Acad. Sci. Paris33 (1908), 1–128.

    Google Scholar 

  5. G. H. Hardy, J. E. Littlewood and G. Pólya,Inequalities, Cambridge Univ. Press, 1959.

  6. J. Hersch,Longueurs extrémales et théorie des fonctions, Comment. Math. Helv.29 (1955), 301–337.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Hersch,Erweiterte Symmetrieeigenschaften von Lösungen gewisser linearer Rand- und Eigenwertprobleme, J. Reine Angew. Math.218 (1965), 143–158.

    MathSciNet  Google Scholar 

  8. J. Hersch,Transplantation harmonique, transplantation par modules, et théorèmes isopérimétriques, Comment. Math. Helv.44 (1969), 354–366.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Hersch.Isoperimetrische, Schranken für die Gebietsabhängigkeit einiger Funktionale der mathematischen Physik, I.S.N.M.39, Birkhäuser Verlag, 1978, pp. 139–161.

  10. M.-Th. Kohler-Jobin,Une propriété de monotonie isopérimétrique qui contient plusieurs thérèmes classiques, C. R. Acad. Sci. Paris A284 (1977), 917.

    MATH  MathSciNet  Google Scholar 

  11. M.-Th. Kohler-Jobin,Une méthode de comparaison isopérimétrique de fonctioneelles de domaines de la physique mathématique, Z. Angew. Math. Phys.29 (1978), 757–776.

    Article  MATH  MathSciNet  Google Scholar 

  12. L. E. Payne,Some isoperimetric inequalities in the torsion problem for multiply connected regions Studies in Math. Analysis and Related Topics (essays in honor of George Pólya), Stanford Univ. Press, 1962, pp. 270–280.

  13. L. E. Payne,Isoperimetric inequalities and their applications, SIAM Rev.9 (1967), 453–488.

    Article  MATH  MathSciNet  Google Scholar 

  14. G. Pólya and G. Szegö,Isoperimetric Inequalities in Mathematical Physics, Princeton Univ. Press, 1951.

  15. M. M. Schiffer,Partial differential equations of elliptic type, Lecture series, Symposium on Partial Differential Equations, Berkeley 1955 (1957), 97–149.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to the memory of Professor Zeev Nehari

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hersch, J. On the torsion function, Green's function and conformal radius: An isoperimetric inequality of Pólya and Szegö, some extensions and applications. J. Anal. Math. 36, 102–117 (1979). https://doi.org/10.1007/BF02798771

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02798771

Keywords

Navigation