Classical Variational Problems

  • Philippe Blanchard
  • Erwin Brüning
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

In many applications of the calculus of variations we have specific information about the form of the functional f which we want to minimise. In practical terms, this means that the functional f has the form
$$f(\varphi ) = \int_I {F(t,\varphi (t),\varphi '(t), \ldots ,{\varphi ^{(n)}}(t))} dt,{\varphi ^{(p)}}(t) = \frac{{{d^p}\varphi }}{{d{t^p}}}(t),$$
where we have a certain function \(F:I \times {\mathbb{R}^{N + 1}} \to \mathbb{R},\varphi :I \to \mathbb{R},\) and a compact interval I= [a, b] or, alternatively, an equivalent generalisation to functions φ of several variables and to functions φ with values in ℝ p , p>1.

Keywords

Manifold Assure Refraction Clarification IRni 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Philippe Blanchard
    • 1
  • Erwin Brüning
    • 2
  1. 1.Theoretische Physik, Fakultät für PhysikUniversität BielefeldBielefeldGermany
  2. 2.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa

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