Advertisement

The Classical Problems of the Calculus of Variations: Necessary Conditions and Sufficient Conditions; Convexity and Lower Semicontinuity

  • Lamberto Cesari
Chapter
Part of the Applications of Mathematics book series (SMAP, volume 17)

Abstract

We are concerned here with classical Lagrange problems of the calculus of variations (see Section 1.1). Precisely, we are concerned with minima and maxima of the functional
$$ I\left[ x \right] = \int_{{{{t}_{1}}}}^{{{{t}_{2}}}} {{{f}_{0}}(t,x(t),x'(t))dt,x(t) = ({{x}^{1}}, \ldots ,{{x}^{n}})} , $$
(2.1.1)
with constraints and boundary conditions
$$\left( {t,x\left( t \right)} \right) \in A,{\text{ t}} \in \left[ {{t_1},{t_2}} \right],{\text{ }}\left( {{t_1},x\left( {{t_1}} \right),{t_2},x\left( {{t_2}} \right)} \right) \in B$$
(2.1.2)

Keywords

Euler Equation Absolute Minimum Absolutely Continuous Canonical Equation Invariant Character 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • Lamberto Cesari
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations