Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

Variation of domain functionals


Author: M. Schiffer
Journal: Bull. Amer. Math. Soc. 60 (1954), 303-328
DOI: https://doi.org/10.1090/S0002-9904-1954-09815-4
MathSciNet review: 0064149
Full-text PDF Free Access

References | Additional Information

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

  • 1. M. Biernacki, Sur la représentation conforme des domaines linéairement accessibles, Prace Math. Fiz. vol. 44 (1936) pp. 293-314.
  • 2. P. R. Garabedian, H. Lewy, and M. Schiffer, Axially symmetric cavitational flow, Ann. of Math. (2) 56 (1952), 560–602. MR 0053684, https://doi.org/10.2307/1969661
  • 3. P. R. Garabedian and M. Schiffer, Convexity of domain functionals, J. Analyse Math. 2 (1953), 281–368. MR 0060117, https://doi.org/10.1007/BF02825640
  • 4. P. R. Garabedian and M. Schiffer, Variational problems in the theory of elliptic partial differential equations, J. Rational Mech. Anal. 2 (1953), 137–171. MR 0054819
  • 5. P. R. Garabedian and D. C. Spencer, Extremal methods in cavitational flow, J. Rational Mech. Anal. 1 (1952), 359–409. MR 0048983
  • 6. G. Golusin, Method of variations in the theory of conformal mapping, Mat. Sbornik N.S. vol. 19 (1946) pp. 203-236; vol. 21 (1947) pp. 83-117, 119-132.
  • 7. J. Hadamard, Mémoire sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées, Mémoires des Savants Etrangers vol. 33 (1908).
  • 8. D. Hilbert, Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, Leipzig, 1912.
  • 9. Gaston Julia, Sur une équation aux dérivées fonctionnelles liée à la représentation conforme, Ann. Sci. École Norm. Sup. (3) 39 (1922), 1–28 (French). MR 1509240
  • 10. J. Leray, Les problèmes de représentation conforme d'Helmholtz; théorie des sillages et des proues, Comment. Math. Helv. vol. 8 (1935) pp. 149-180, 250-263.
  • 11. Karl Löwner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann. 89 (1923), no. 1-2, 103–121 (German). MR 1512136, https://doi.org/10.1007/BF01448091
  • 12. G. C. Nooney, On the vibrations of triangular membranes, Technical Report No. 35, Office of Naval Research Contract N6ori-106 Task Order V, Stanford University.
  • 13. G. Pólya and G. Szegö, Isoperimetric inequalities of mathematical physics, Princeton, 1951.
  • 14. G. Pólya and M. Schiffer, Convexity of functionals by transplantation, J. Analyse Math. 3 (1954), 245–346. With an appendix by Heinz Helfenstein. MR 0066530, https://doi.org/10.1007/BF02803593
  • 15. H. Poincaré, Figures d'équilibre d'une masse fluide, Paris, 1902.
  • 16. R. de Possel, Zum Parallelschlitztheorem unendlich-vielfach zusammenhängender Gebiete, Göttinger Nachr. (1931) pp. 199-202.
  • 17. J. W. Rayleigh, The theory of sound, 2d ed., London, 1894.
  • 18. D. Riabouchinsky, Sur un problème de variation, C. R. Acad. Sci. Paris vol. 185 (1927) pp. 840-841.
  • 19. A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, American Mathematical Society Colloquium Publications, Vol. 35, American Mathematical Society, New York, N. Y., 1950. With a Chapter on the Region of the Derivative of a Schlicht Function by Arthur Grad. MR 0037908
  • 20. Menahem Schiffer, Variational methods in the theory of conformal mapping, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R. I., 1952, pp. 233–240. MR 0045215
  • 21. Menahem Schiffer and Donald C. Spencer, Functionals of finite Riemann surfaces, Princeton University Press, Princeton, N. J., 1954. MR 0065652
  • 22. M. Schiffer and G. Szegö, Virtual mass and polarization, Trans. Amer. Math. Soc. 67 (1949), 130–205. MR 0033922, https://doi.org/10.1090/S0002-9947-1949-0033922-9
  • 23. O. Teichmüller, Ungleichungen zwischen den Koeffizienten schlichter Funktionen, Preuss. Akad. Wiss. Sitzungsber. Phys.-math. Klasse (1938) pp. 363-375.


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1954-09815-4