The Development of Sufficient Conditions in the Calculus of Variations ... |
Contents
Chapter | 2 |
The state of the theory just prior to | 4 |
THE FIELD METHOD OF WEIERSTRASS FOR SIMPLE PROBLEMS | 28 |
7 other sections not shown
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Common terms and phrases
A₁ admissible arcs joining admissible sets analogue arc E12 Bliss Bolza calculus of variations Caratheodory Chapter class C12 class of arcs comparison arcs corners covers a region curve curvilinear coordinates defined derived differential equation E-function existence theorem expansion method expansion proof extremal arc family of extremals family of geodesically field method fundamental sufficiency theorem G. A. Bliss geodesic Hahn Hamilton-Jacobi theory Hilbert integral holds inequality 16 integrand isoperimetric problem Jacobi condition joining the points Kneser Lagrange problem Legendre Legendre's lemma Lindeberg Mayer field method of Weierstrass minimizing arc n-parameter family necessary condition neighborhood non-parametric non-parametric problem Osgood parametric form parametric problem problem of Lagrange proved published region F respect to admissible satisfies the conditions Scheeffer second variation simply covers slope functions strong relative minimum suffi sufficiency proofs sufficient conditions surface t₁ tion Tonelli variable end points weak relative minimum writers X₁ X₂ Y₁ Zermelo