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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
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  • 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. vol. 56 (1952) pp. 560-602. MR 53684
  • 3. P. R. Garabedian and M. Schiffer, Convexity of domain Junctionals, Journal d'Analyse Mathématique vol. 2 (1953) pp. 281-368. MR 60117
  • 4. P. R. Garabedian and M. Schiffer, Variational problems in the theory of elliptic partial differential equations, Journal of Rational Mechanics and Analysis vol. 2 (1953) pp. 137-171. MR 54819
  • 5. P. R. Garabedian and D. C. Spencer, Extremal methods in cavitational flow, Journal of Rational Mechanics and Analysis vol. 1 (1952) pp. 359-409. MR 48983
  • 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, Journal d'Analyse Mathématique, to appear. MR 66530
  • 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, Amer. Math. Soc. Colloquium Publications, vol. 35, New York, 1950. MR 37908
  • 20. M. Schiffer, Variational methods in the theory of conformal mapping, Proceedings of the International Congress of Mathematicians 1950, vol. II, pp. 233-240. MR 45215
  • 21. M. Schiffer and D. C. Spencer, Functionals of finite Riemann surfaces, Princeton, 1954. MR 65652
  • 22. M. Schiffer and G. Szegö, Virtual mass and polarization, Trans. Amer. Math. Soc. vol. 67 (1949) pp. 130-205. MR 33922
  • 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

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