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A saint-venant principle for the gradient in the Neumann problem

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Abstract

The maximum principle for subharmonic functions is used to obtain upper bounds for the gradient in the Neumann problem of potential theory. These bounds, which concern a curvilinear strip domain having nonzero boundary data only on an end, entail an exponential decay of the gradient magnitude with distance from that end.

Zusammenfassung

Unter Benutzung des Maximumprinzips für subharmonische Funktionen werden obere Schranken angegeben für den Gradienten des Neumannschen Problems der Potential-Theorie. Diese Schranken betreffen einem gekrümmten Streifenbereich mit von Null verschiedenen Grenzdaten an einem Ende und haben zur Folge, dass der Betrag des Gradienten exponentiell mit dem Abstand von diesem Ende abfällt.

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Author notes

  1. Matías J. Turteltaub

    Present address: Facultad de Ingeniería, Escuela Basica-Dpto. de Mecánica, Universidad Central de Venezuela, Ciudad Universitaria, Caracas, Venezuela

Authors and Affiliations

  1. Dept. of Mechanical Engineering, University of Houston, Houston, USA

    Lewis T. Wheeler, Matías J. Turteltaub & Cornelius O. Horgan

Authors
  1. Lewis T. Wheeler
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  2. Matías J. Turteltaub
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  3. Cornelius O. Horgan
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Wheeler, L.T., Turteltaub, M.J. & Horgan, C.O. A saint-venant principle for the gradient in the Neumann problem. Journal of Applied Mathematics and Physics (ZAMP) 26, 141–153 (1975). https://doi.org/10.1007/BF01591502

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  • DOI: https://doi.org/10.1007/BF01591502

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