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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Variational problems within the class of solutions of a partial differential equation
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by Robert Delver PDF
Trans. Amer. Math. Soc. 180 (1973), 265-289 Request permission

Abstract:

The subject of this paper is the optimization of a multiple integral over a domain $G$ of a function, containing as arguments the independent variables, the unknown function and its partial derivatives up to order $l$, within the class of all sufficiently smooth solutions in $G$ of a given partial differential equation of order greater than or equal to $2l$. Necessary conditions in the form of a boundary value problem are derived. A physical application occurs in the control with boundary and initial conditions of a process in $G$ that is described by a specific partial differential equation.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 180 (1973), 265-289
  • MSC: Primary 49B15
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0320856-9
  • MathSciNet review: 0320856