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Direct Methods of the Calculus of Variations

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Book cover Variational Methods in Mathematical Physics

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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

  1. Lebesgue, H.: Sur le problème de Dirichlet. Rend. Circ. mat. Palermo bf 24 (1905) 371–402

    Article  Google Scholar 

  2. Schäfer, H.: Topological vector spaces. Springer, Berlin Heidelberg 1971

    Google Scholar 

  3. Vainberg, M.M.: Variational methods for the study of nonlinear operators. Holden Day, London 1964

    MATH  Google Scholar 

  4. Carrol, R.W.: Abstract methods in partial differential equations. Harper and Row, New York 1969

    Google Scholar 

  5. Berger, M.S.: Non-linearity and functional analysis. Academic Press, New York 1977

    Google Scholar 

  6. Choquet, G.: Lectures on analysis II. Benjamin, New York 1969

    MATH  Google Scholar 

  7. Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. J. reine angew. Math. 135 (1908) 1–61

    MATH  Google Scholar 

  8. Courant, R., Hilbert, D.: Methods of mathematical physics. Wiley-Interscience, New York 1966

    Google Scholar 

  9. 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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