Beiträge zur Theorie und Anwendung der Variationsrechnung. (Zweiter Aufsatz).
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Adolf Kneser (1903)
Mathematische Annalen
Adolf Kneser (1902)
Mathematische Annalen
W. Ermakoff (1905)
Journal de Mathématiques Pures et Appliquées
Odzijewicz, Tatiana, Torres, Delfim F. M. (2012)
Mathematica Balkanica New Series
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.
Steven Verpoort (2011)
Czechoslovak Mathematical Journal
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.
R.G.D. Richardson (1910)
Mathematische Annalen
Mayer (1870)
Mathematische Annalen
Mayer (1878)
Mathematische Annalen
Scheeffer (1885)
Mathematische Annalen
Mititelu, Ştefan (2008)
APPS. Applied Sciences
F. Österreicher, M. Thaler (1980)
Monatshefte für Mathematik
Oskar Bolza (1907)
Mathematische Annalen
Svetlichny, George (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Fusco, N., Marcellini, P., Ornelas, A. (1998)
Portugaliae Mathematica
Giovanni Cupini, Marcello Guidorzi, Cristina Marcelli (2009)
Annales de l'I.H.P. Analyse non linéaire
Rocha, Eugénio A.M., Torres, Delfim F.M. (2008)
APPS. Applied Sciences
G. Bliß (1904)
Mathematische Annalen
Georg Landsberg (1907)
Jahresbericht der Deutschen Mathematiker-Vereinigung
Adolf Kneser (1900)
Giovanni Cupini, Cristina Marcelli (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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.
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