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Three-dimensional subsonic flows, and asymptotic estimates for elliptic partial differential equations

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Acta Mathematica

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References

  1. Bers, L., Existence and uniqueness of a subsonic flow past a given profile.Comm. Pure Appl. Math., 7 (1954), 441–504.

    MATH  MathSciNet  Google Scholar 

  2. Bers, L.,THeory of Pseudo-analytic Functions. Lecture notes (mimeographed). New York University, 1953.

  3. Chaplygin, S. A., On gas jets.Sci. Mem. Imp. Univ. Moscow, Math. Phys. Sec., 21 (1902), 1–121.

    Google Scholar 

  4. Cordes, H. O., Über die erste Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen.Math. Ann. 130 (1956), 278–312.

    Article  MathSciNet  Google Scholar 

  5. Finn, R., Isolated singularities of solutions of non-linear partial differential equations.Trans. Amer. Math. Soc., 75 (1953), 385–404.

    Article  MATH  MathSciNet  Google Scholar 

  6. Finn, R. & Gilbarg, D., Asymptotic behavior and uniqueness of plane subsonic flows.Comm. Pure Appl. Math. (to appear).

  7. Frankl, F. I. &Keldysh, M., Die äussere Neumann'sche Aufgabe für nichtlineare elliptische Differentialgleichungen mit Anwendung auf die Theorie der Flügel im kompressiblen Gas.Bull. Acad. Sci., URSS, 12 (1934), 561–607.

    Google Scholar 

  8. Gilbarg, D. &Shiffman, M., On bodies achieving extreme values of the Critical Mach number I.J. Rational Mech. Anal., 3 (1954), 209–230.

    MathSciNet  Google Scholar 

  9. Hardy, G. H., Littlewood, J. E. & Polya, G.,Inequalities. Cambridge Univ. Press, (1934).

  10. Hopf, E., Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus.Stizungsber.Berl. Akad. Wiss., 19 (1927), 147–152.

    Google Scholar 

  11. Leray, J. &Schauder, J., Topologie et équations fonctionnelles.Ann. Ecole Norm., 51 (1934), 45–78.

    MathSciNet  Google Scholar 

  12. Lichtenstein, L., Neuere Entwicklung der Potentialtheorie.Enc. Math. Wiss., Band II, 3. Teil, 1. Hälfte, Leipzig, 1909–1921, pp. 181 ff.

    Google Scholar 

  13. Ludford, G. S. S., D'Alembert's paradox and the moment formula in three-dimensional subsonic flow.Rev. Fac. Sci. Univ. Istanbul, Ser. A, 18 (1953), 1–13.

    MATH  MathSciNet  Google Scholar 

  14. Miranda, C.,Equazioni alle derivate parziali di tipo ellitico, p. 171. Springer-Verlag, 1955.

  15. Morrey, C. B., On the solutions of quasi-linear elliptic partial differential equations.Trans. Amer. Math. Soc., 43 (1938), 126–166.

    Article  MATH  MathSciNet  Google Scholar 

  16. Schauder, J., Der Fixpunktsatz in Funktionalräumen.Studia Math., 2 (1930), 171–130.

    MATH  Google Scholar 

  17. —, Equations du type elliptique, problèmes linéares.L'Enseign. Math., 35 (1936), 126–139, esp. 138.

    MATH  Google Scholar 

  18. Shiffman, M., Differentiability and analyticity of solutions of double integral variational problems.Ann. of Math., 48 (1947), 274–284.

    Article  MATH  MathSciNet  Google Scholar 

  19. —, On the existence of subsonic flows of a compressible fluid.J. Rational Mech. Anal., 1 (1952), 605–652.

    MATH  MathSciNet  Google Scholar 

  20. Tonelli, L., L'estremo assoluto degli integrali doppi.Ann. Scuola Norm. Super. Pisa, 2 (1933), 89–130.

    MATH  Google Scholar 

  21. Payne, L. E. &Weinberger, H. F., Note on a lemma of Finn and Gilbarg,Acta Math., 98 (1957), 297–299.

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Southern California, California, USA

    Robert Finn

  2. California Institute of Technology, California, USA

    Robert Finn

  3. Indiana University, Indiana, USA

    David Gilbarg

  4. Stanford University, Stanford, USA

    David Gilbarg

Authors
  1. Robert Finn
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  2. David Gilbarg
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Additional information

This investigation was supported by the Office of Naval Research.

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Finn, R., Gilbarg, D. Three-dimensional subsonic flows, and asymptotic estimates for elliptic partial differential equations. Acta Math. 98, 265–296 (1957). https://doi.org/10.1007/BF02404476

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