Abstract
In an earlier chapter, the functional equation technique of dynamic programming was applied to obtain a variational equation for a Green’s function corresponding to a second order ordinary differential equation. In the present chapter, this method is extended to apply to elliptic partial differential operators, and a first consequence is the classical Hadamard variational formula.
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Bibliography and Comments
R. Bellman and H. Osborn, ’Dynamic Programming and the Variation of Green’s Functions’. Journal of Mathematics and Mechanics 7 (1958), 81–85.
S.E. Dreyfus, Dynamic Programming and the Calculus of Variations, Academic Press, Inc., New York, 1965.
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© 1985 D. Reidel Publishing Company
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Bellman, R., Adomian, G. (1985). The Hadamard Variational Formula. In: Partial Differential Equations. Mathematics and Its Applications, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5209-6_7
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DOI: https://doi.org/10.1007/978-94-009-5209-6_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8804-6
Online ISBN: 978-94-009-5209-6
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