Isolated singularities of solutions of non-linear partial differential equations
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- by Robert Finn
- Trans. Amer. Math. Soc. 75 (1953), 385-404
- DOI: https://doi.org/10.1090/S0002-9947-1953-0058826-8
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References
- S. A. Chaplygin, On gas jets, Sci. Mem. Imp. Univ. Moscow Math. Phys. Sec. vol. 21 (1904).
- Lipman Bers, Isolated singularities of minimal surfaces, Ann. of Math. (2) 53 (1951), 364–386. MR 43335, DOI 10.2307/1969547
- Lipman Bers, Singularities of minimal surfaces, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R.I., 1952, pp. 157–164. MR 0050190
- Lipman Bers, Abelian minimal surfaces, J. Analyse Math. 1 (1951), 43–58. MR 43336, DOI 10.1007/BF02790082
- Serge Bernstein, Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus, Math. Z. 26 (1927), no. 1, 551–558 (German). MR 1544873, DOI 10.1007/BF01475472
- Tibor Radó, Zu einem Satze von S. Bernstein über Minimalflächen im Großen, Math. Z. 26 (1927), no. 1, 559–565 (German). MR 1544874, DOI 10.1007/BF01475473
- Eberhard Hopf, On S. Bernstein’s theorem on surfaces $z(x,y)$ of nonpositive curvature, Proc. Amer. Math. Soc. 1 (1950), 80–85. MR 35803, DOI 10.1090/S0002-9939-1950-0035803-7
- Earl J. Mickle, A remark on a theorem of Serge Bernstein, Proc. Amer. Math. Soc. 1 (1950), 86–89. MR 35804, DOI 10.1090/S0002-9939-1950-0035804-9 H. Bateman, Partial differential equations of mathematical physics, p. 135. T. Carleman, Sur les systèmes linéaires aux dérivées partielles du premier ordre à deux variables, C. R. Acad. Sci. Paris vol. 197 (1933) pp. 471-474.
- J. Schauder, Über das Dirichletsche Problem im Großen für nicht-lineare elliptische Differentialgleichungen, Math. Z. 37 (1933), no. 1, 623–634 (German). MR 1545424, DOI 10.1007/BF01474604 T. Radó, Geometrische Betrachtungen über reguläre Variationsprobleme, Acta Univ. Szeged, vol. 2 (1924/26) pp. 228-254. J. von Neumann, Über einen Hilfsatz der Variationsrechnung, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg vol. 8 (1931) pp. 28-31.
- Jean Leray and Jules Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. (3) 51 (1934), 45–78 (French). MR 1509338, DOI 10.24033/asens.836
- Jean Leray, Discussion d’un problème de Dirichlet, J. Math. Pures Appl. (9) 18 (1939), 249–284 (French). MR 0001094
- Max Shiffman, Differentiability and analyticity of solutions of double integral variational problems, Ann. of Math. (2) 48 (1947), 274–284. MR 21256, DOI 10.2307/1969170
- Charles B. Morrey Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), no. 1, 126–166. MR 1501936, DOI 10.1090/S0002-9947-1938-1501936-8
- Eberhard Hopf, Zum analytischen Charakter der Lösungen regulärer zweidimensionaler Variationsprobleme, Math. Z. 30 (1929), no. 1, 404–413 (German). MR 1545070, DOI 10.1007/BF01187779 R. Courant and D. Hilbert, Mathematische Physik, vol. II, pp. 276-277. A. Gelbart, On a function-theory method for obtaining potential flow patterns of a compressible fluid, NACA Report ARR No. 3G27, July, 1943.
Bibliographic Information
- © Copyright 1953 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 75 (1953), 385-404
- MSC: Primary 36.0X
- DOI: https://doi.org/10.1090/S0002-9947-1953-0058826-8
- MathSciNet review: 0058826