Abstract
In our previous chapter we showed that the determination of the extrema, such as the minima, of a function, is central to the calculus of variations. An extreme value problem in its most general form can be understood to be the following.
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References
Lebesgue, H.: Sur le problème de Dirichlet. Rend. Circ. mat. Palermo bf 24 (1905) 371–402
Schäfer, H.: Topological vector spaces. Springer, Berlin Heidelberg 1971
Vainberg, M.M.: Variational methods for the study of nonlinear operators. Holden Day, London 1964
Carrol, R.W.: Abstract methods in partial differential equations. Harper and Row, New York 1969
Berger, M.S.: Non-linearity and functional analysis. Academic Press, New York 1977
Choquet, G.: Lectures on analysis II. Benjamin, New York 1969
Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. J. reine angew. Math. 135 (1908) 1–61
Courant, R., Hilbert, D.: Methods of mathematical physics. Wiley-Interscience, New York 1966
Cea, J.: Optimisation, théorie et algorithmes. Dunod, Paris 1971. Optimisa-tion techniques, Proc. 7th IFIP Conf., Nice 1975. Springer, Berlin Heidelberg 1976
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© 1992 Springer-Verlag Berlin Heidelberg
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Blanchard, P., Brüning, E. (1992). Direct Methods of the Calculus of Variations. In: Variational Methods in Mathematical Physics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82698-6_2
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DOI: https://doi.org/10.1007/978-3-642-82698-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82700-6
Online ISBN: 978-3-642-82698-6
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