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Feldtheorie in der Variationsrechnung Mehrfacher Integrale

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Abstract

The theory of geodesic fields of VAGNER [12] and LIESEN [10] evidently yields the best results in comparison with the field theories of the LEPAGEan bundle. We try to elucidate the theory form a FINSLER-geometric point of view and to make it better applicable. A regularity condition analogous to the HADAMARD sufficient Legendre-condition is deduced, which is less restrictive than the conditions of the original CARATHEODORY and de DONDER-WEYL field theories. Local geodesic fields are constructed. We give a sufficient Legendre-and Weierstraß-condition and finally discuss the scope of field theory.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Klinikstr. 6, 87 Würzburg

    U. Brechtken-Manderscheid

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  1. U. Brechtken-Manderscheid
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Herrn Professor Dr. Dr. Otto Volk zum 80. Geburtstag am 13. Juli 1972 gewidmet

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Brechtken-Manderscheid, U. Feldtheorie in der Variationsrechnung Mehrfacher Integrale. Manuscripta Math 7, 87–102 (1972). https://doi.org/10.1007/BF01303539

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  • DOI: https://doi.org/10.1007/BF01303539

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