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The First Variation

  • Mariano Giaquinta
  • Stefan Hildebrandt
Chapter
  • 2.3k Downloads
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 310)

Abstract

In this chapter we shall develop the formalism of the calculus of variations in simple situations. After a brief review of the necessary and sufficient conditions for extrema of ordinary functions on ℝ n , we investigate in Section 2 some of the basic necessary conditions that are to be satisfied by minimizers of variational integrals
$$ \mathcal{F}(u) = \int_\Omega {F(x,u(x),Du(x)dx)} $$
(1)
.

Keywords

Euler Equation Variational Problem Variational Integral Rotation Number Admissible Function 
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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mariano Giaquinta
    • 1
  • Stefan Hildebrandt
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Mathematisches InstitutUniversität BonnBonnGermany

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