Beiträge zur Theorie und Anwendung der Variationsrechnung. (Zweiter Aufsatz).
Beiträge zur Theorie und Anwendung der Variationsrechnung. (Erster, Aufsatz) .
Calcul des variations d'après Weierstrass
Calculus of Variations with Classical and Fractional Derivatives
MSC 2010: 49K05, 26A33We give a proper fractional extension of the classical calculus of variations. Necessary optimality conditions of Euler-Lagrange type for variational problems containing both classical and fractional derivatives are proved. The fundamental problem of the calculus of variations with mixed integer and fractional order derivatives as well as isoperimetric problems are considered.
Curvature functionals for curves in the equi-affine plane
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.
Das Jacobische Kriterium der Variationsrechnung und die Oszillationseigenschaften linearer Differentialgleichungen 2. Ordnung. (Mit 1 Figur im Text) .
Der Satz der Variationsrechnung, welcher dem Princip der kleinsten Wirkung in der Mechanik entspricht.
Die Kriterien des Maximums und Minimums der einfachen Integrale in den isoperimetrischen Problemen. (Aus den Ber. der Kgl. Sächs. Ges. d. Wiss. Juli 1877)
Die Maxima und Minima der einfachen Integrale zwischen festen Grenzen
Efficiency conditions for multiobjective fractional variational problems.
Ein Beitrag zur Suche der Extremstelle einer strikt unimodalen Funktion.
Ein Satz über eindeutige Abbildung und seine Anwendung in der Variationsrechnung
Equivariance, variational principles, and the Feynman integral.
Existence of minimizers for some non convex one-dimensional integrals.
Existence of minimizers of free autonomous variational problems via solvability of constrained ones
First integrals for problems of calculus of variations on locally convex spaces.
Jacobi's Criterion when both end-points are variable
Krümmungstheorie und Variationsrechnung.
Lehrbuch der Variationsrechnung [Book]
Monotonicity properties of minimizers and relaxation for autonomous variational problems
We consider the following classical autonomous variational problemwhere the Lagrangianf is possibly neither continuous, nor convex, nor coercive. We prove a monotonicity property of the minimizers stating that they satisfy the maximum principle or the minimum one. By virtue of such a property, applying recent results concerning constrained variational problems, we derive a relaxation theorem, the DuBois-Reymond necessary condition and some existence or non-existence criteria.