Theses on the Calculus of Variations Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy, Department of Mathematics1933 - Calculus of variations - 426 pages |
Contents
ANALOGUE OF THE EDGE CONDITIONS | 9 |
ISOPERIMETRIC PROBLEM THE LAGRANGE MULTI | 24 |
ANALOGUE OF THE EDGE CONDITIONS FOR THE 180 | 29 |
7 other sections not shown
Common terms and phrases
admissible arc admissible variations analogue arguments boundary value problem C₂ calculus of variations characteristic numbers coefficients conjugate point continuous corner corollary corresponding curve defined definition determinant different from zero differential equations discontinuous double integral E₁₂ end conditions Euler-Lagrange equations exists expression extremaloid finite number Fischer focal point follows Fréchet func functional F functions of lines given Hence hypothesis identically zero integrand interval isoperimetric problem Jacobi condition Lagrange problem lemma Lincei linear functional linearly independent manifold matrix maximizing arc minimizing arc minimizing surface minimum monopoly problem multiplier rule necessary condition neighborhood normal P₁ parameter values partial derivatives problem of Lagrange problem of Mayer problem of minimizing proof properties quadratic form respect Riesz theorem satisfy the equations satisfying the conditions second variation semi-extremal solution of equation Stieltjes integral sufficient conditions theorem tions vanish variable Volterra x₁ x₁(y x₂ y₁