A Saint-Venant principle for a class of second-order elliptic boundary value problems


Ein Saint-Venantsches Prinzip für eine gewisse Art von Randwertproblemen elliptischer Differentialgleichungen zweiter Ordnung wird bewiesen. Der Beweis erfordert die Abschätzung verschiedener energie-artiger Funktionale, die zur Herleitung von lokalen Schranken für die Lösung erforderlich sind. Zur Veranschaulichung wird das Prinzip auf die Berechnung der Kanalströmung einer zähigkeitslosen Flüssigkeit angewendet.

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This research was supported in part by the United States Office of Naval Research under Contract Nonr 220(56). Reproduction in whole or in part is permitted for any purpose of the United States Government.

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Knowles, J.K. A Saint-Venant principle for a class of second-order elliptic boundary value problems. Journal of Applied Mathematics and Physics (ZAMP) 18, 473–490 (1967). https://doi.org/10.1007/BF01601718

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  • Mathematical Method
  • Elliptic Boundary