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Garabedian, P. R.; Schiffer, M.

Convexity of domain functionals. (English) Zbl 0052.33203

J. Anal. Math. 2, 281-368 (1953).
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Keywords:

partial differential equations
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\textit{P. R. Garabedian} and \textit{M. Schiffer}, J. Anal. Math. 2, 281--368 (1953; Zbl 0052.33203)
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References:

[1] Bergman, S., ”The kernel function and conformal mapping”,Amer. Math. Soc. Survey, New York, 1950. · Zbl 0040.19001
[2] Bergman, S. and Schiffer, M.,Kernel functions in mathematical physics, Academic Press, New York, 1953. · Zbl 0053.39003
[3] Carathéodory, C.,Conformal representation, Cambridge, 1952. · Zbl 0047.07905
[4] Courant, R. and Hilbert, D.,Methoden der mathematischen Physik, New York, 1943. · Zbl 0061.16602
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[6] Friedrichs, K., ”Ueber ein Minimumproblem für Potentialströmungen mit freiem Rande”,Math. Ann., Vol. 109 (1933–34), pp. 60–82. · JFM 59.1447.01
[7] Garabedian, P. R., Lewy, H. and Schiffer, M., ”Axially symmetric cativational flow”,Ann. Math. Vol. 56 (1952), pp. 560–602. · Zbl 0047.18203
[8] Garabedian, P. R. and Schiffer, M., ”Variational problems in the theory of elliptic partial differential equations”,J. Ratl. Mech. and Anal., Vol. 2 (1953), pp. 137–171. · Zbl 0050.10002
[9] Garabedian, P. R. and Spencer, D. C., ”Extremal methods in cavitational flow”.J. Ratl. Mech. and Anal., Vol. 1 (1952), pp. 359–409. · Zbl 0046.18504
[10] Hadamard, J., ”Mémorie sur le problème d’analyse relatif à l’équilibre des plaques élastiques encastrées”,Mémoires des savants étrangers, Vol. 33 (1908). · JFM 39.1022.01
[11] Hilbert, D.,Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, Leipzig, 1912.
[12] Jeans, J. H.,The mathematical theory of electricity and magnetism, Cambridge, 1908. · JFM 39.0951.05
[13] Milne-Thomson, L. M.,Theoretical aerodynamics, New York, 1948. · Zbl 0029.28204
[14] Morse, M.,The calculus of variations in the large, New York, 1934. · Zbl 0011.02802
[15] Poincaré, H.,Figures d’équilibre d’une masse fluide, Paris, 1902. · JFM 33.0744.04
[16] Pólya, G. and Szegö, G.,Isoperimetric inequalities in mathematical physics, Princeton, 1951. · Zbl 0044.38301
[17] Rayleigh, J. W.,The theory of sound, New York, 1945. · Zbl 0061.45904
[18] Schiffer, M., ”Hadamard’s formula and variation of domain functions”,Amer. J. Math., Vol. 68 (1946), pp. 417–448. · Zbl 0060.23706
[19] Schiffer, M. and Szegö, G., ”Virtual mass and polarization,”Trans. Amer. Math., Soc. Vol. 67 (1949), pp. 130–205. · Zbl 0035.11803
[20] Shiffman, M., ”The Plateau problem for non-relative minima”,Ann. Math. Vol. 40 (1939), pp. 834–854. · Zbl 0023.39802
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