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Direct Methods of the Calculus of Variations

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Part of the Texts and Monographs in Physics book series (TMP)

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.

Keywords

Banach Space Lower Semicontinuous Fundamental Theorem Weak Topology Hausdorff Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.1
    Lebesgue, H.: Sur le problème de Dirichlet. Rend. Circ. mat. Palermo bf 24 (1905) 371–402CrossRefGoogle Scholar
  2. 1.2
    Schäfer, H.: Topological vector spaces. Springer, Berlin Heidelberg 1971Google Scholar
  3. 1.3
    Vainberg, M.M.: Variational methods for the study of nonlinear operators. Holden Day, London 1964zbMATHGoogle Scholar
  4. 1.4
    Carrol, R.W.: Abstract methods in partial differential equations. Harper and Row, New York 1969Google Scholar
  5. 1.5
    Berger, M.S.: Non-linearity and functional analysis. Academic Press, New York 1977Google Scholar
  6. 1.6
    Choquet, G.: Lectures on analysis II. Benjamin, New York 1969zbMATHGoogle Scholar
  7. 1.7
    Ritz, W.: Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. J. reine angew. Math. 135 (1908) 1–61zbMATHGoogle Scholar
  8. 1.8
    Courant, R., Hilbert, D.: Methods of mathematical physics. Wiley-Interscience, New York 1966Google Scholar
  9. 1.9
    Cea, J.: Optimisation, théorie et algorithmes. Dunod, Paris 1971. Optimisa-tion techniques, Proc. 7th IFIP Conf., Nice 1975. Springer, Berlin Heidelberg 1976Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Theoretische Physik, Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa

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