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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Isoperimetric inequalities involving heat flow under linear radiation conditions
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by Andrew Acker PDF
Proc. Amer. Math. Soc. 64 (1977), 265-271 Request permission

Abstract:

Under the assumption that a constant linear radiation condition holds on each boundary component, we show that the annulus and the strip are heat-flow minimizing with respect to area-preserving variations in one (for the annulus: the outer) boundary component.
References
  • Andrew Acker, Heat flow inequalities with applications to heat flow optimization problems, SIAM J. Math. Anal. 8 (1977), no. 4, 604–618. MR 473960, DOI 10.1137/0508048
  • T. Carleman, Über ein Minimalproblem der mathematischen Physik, Math. Z. 1 (1918), no. 2-3, 208–212 (German). MR 1544292, DOI 10.1007/BF01203612
  • G. M. Golusin, Geometrische Funktionentheorie, Hochschulbücher für Mathematik, Band 31, VEB Deutscher Verlag der Wissenschaften, Berlin, 1957 (German). MR 0089896
  • J. Horn, Partielle Differentialgleichungen, Walter de Gruyter & Co., Berlin, 1949 (German). 4th ed. MR 0037983
  • N. I. Mushelišvili, Singular integral equations, Noordhoff, Groningen, 1953.
  • W. Pogorzelski, Integral equations and their applications. Vol. I, International Series of Monographs in Pure and Applied Mathematics, Vol. 88, Pergamon Press, Oxford-New York-Frankfurt; PWN—Polish Scientific Publishers, Warsaw, 1966. Translated from the Polish by Jacques J. Schorr-Con, A. Kacner and Z. Olesiak. MR 0201934
  • G. Szegö, Über einige Extremalaufgaben der Potentialtheorie, Math. Z. 31 (1930), no. 1, 583–593 (German). MR 1545137, DOI 10.1007/BF01246436
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 265-271
  • MSC: Primary 35J99; Secondary 49H05
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0445122-1
  • MathSciNet review: 0445122