Jan Chrastina, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic
Abstract: The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain results resembling the common Euler-Lagrange, Legendre, Jacobi, and Hilbert-Weierstrass conditions whenever possible and to discuss some modifications necessary in the degenerate case. The inverse and the realization problems are mentioned, too.
Keywords: variational integral, critical curve, adjoint module, diffiety, initial form, Poincare-Cartan form, Lagrange problem, Mayer field, Weierstrass function
Classification (MSC 1991): 49-01, 49K15, 58A10, 49N45
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.