The Development of Sufficient Conditions in the Calculus of Variations ... |
Contents
INTRODUCTION | 249 |
The state of the theory just prior to | 263 |
THE FIELD METHOD OF WEIERSTRASS FOR SIMPLE PROBLEMS | 278 |
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Common terms and phrases
a₁ admissible arcs joining admissible sets analogue arc C₁₂ arc E12 Bolza calculus of variations Caratheodory Chapter class C12 class of arcs comparison arcs covers a region curve curvilinear coordinates defined derived differential equations double integrals E-function E₁₂ Euler existence theorem expansion method expansion proof extremal arc family of extremals family of geodesically field method fundamental sufficiency theorem furnishes a strong geodesic Hahn Hamilton-Jacobi theory Hilbert integral holds inequality integrand isoperimetric problem Jacobi condition joining the points Kneser Lagrange problem Legendre Mayer field method of Weierstrass minimizing arc n-parameter family n-space necessary condition neighborhood non-parametric non-parametric problem Osgood parametric problem problem of Lagrange proved rectifiable arcs region F satisfies the conditions Scheeffer's second variation simply covers slope functions solution strong relative minimum suffi sufficiency proofs sufficient conditions surface t₁ tions Tonelli transversals variable end-points weak relative minimum X₁ X₂ Y₁ Zermelo λα