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Transactions of the American Mathematical Society

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



Variational problems within the class of solutions of a partial differential equation

Author: Robert Delver
Journal: Trans. Amer. Math. Soc. 180 (1973), 265-289
MSC: Primary 49B15
MathSciNet review: 0320856
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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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Keywords: Calculus of variations, optimization problems, boundary control of partial differential equations, variational adjoint, associated boundary value problem, necessary conditions
Article copyright: © Copyright 1973 American Mathematical Society