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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A maximum principle for compressible flow on a surface
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by Lesley M. Sibner and Robert J. Sibner PDF
Proc. Amer. Math. Soc. 71 (1978), 103-108 Request permission

Abstract:

We show that the speed of a steady, irrotational, subsonic flow on a surface cannot attain its maximum at a point of positive Gauss curvature.
References
  • Lipman Bers, Mathematical aspects of subsonic and transonic gas dynamics, Surveys in Applied Mathematics, Vol. 3, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096477
  • L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications, Convegno Internazionale sulle Equazioni Lineari alle Derivate Parziali, Trieste, 1954, Edizioni Cremonese, Roma, 1955, pp. 111–140. MR 0076981
  • S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. 52 (1946), 776–797. MR 18022, DOI 10.1090/S0002-9904-1946-08647-4
  • E. Hopf, Elementare Bemerkungen über die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, S.-B. Preuss. Akad. Wiss. Physik-Math. Kl. 19 (1927), 147-152.
  • L. M. Sibner and R. J. Sibner, A non-linear Hodge-de-Rham theorem, Acta Math. 125 (1970), 57–73. MR 281231, DOI 10.1007/BF02392330
  • Lesley M. Sibner, Non-linear Hodge theory: compact manifolds, Global analysis and its applications (Lectures, Internat. Sem. Course, Internat. Centre Theoret. Phys., Trieste, 1972) Internat. Atomic Energy Agency, Vienna, 1974, pp. 121–127. MR 0436186
  • —, Non-linear Hodge theory: Applications, Advances in Math. (to appear). —, Transonic flow on an axiallysymmetric torus, J. Math. Anal. Appl. (to appear).
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 103-108
  • MSC: Primary 58A10; Secondary 58G10
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0482795-2
  • MathSciNet review: 0482795