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Russian Mathematical Surveys, 2011, Volume 66, Issue 4, Pages 733–765
DOI: https://doi.org/10.1070/RM2011v066n04ABEH004754 (Mi rm9429) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Theory of fields of extremals for multiple integrals

M. I. Zelikinab

a Moscow State University
b Steklov Mathematical Institute of the Russian Academy of Sciences
English version PDF (591 kB) Citations (4) Russian version article
References:
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DOI: https://doi.org/10.1070/RM2011v066n04ABEH004754
Abstract: A general theory unifying and generalizing the field theories for multiple integrals due to Weyl and Carathéodory is developed. Generalizations of the Legendre, Weyl, and Carathéodory transforms are introduced, as well as the associated connection and curvature on the fibre bundle underlying the multiple integrals.
Bibliography: 33 titles.
Keywords: field of extremals, Weierstrass function, Legendre transform, connection and curvature on fibre bundles, covariant differentiation.
Received: 14.09.2010
Bibliographic databases:
Document Type: Article
UDC: 517.972
MSC: 34A26, 49K20, 58E15
Language: English
Original paper language: Russian
Citation: M. I. Zelikin, “Theory of fields of extremals for multiple integrals”, Russian Math. Surveys, 66:4 (2011), 733–765
Citation in format AMSBIB
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\paper Theory of fields of extremals for multiple integrals
\jour Russian Math. Surveys
\yr 2011
\vol 66
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\pages 733--765
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  • https://www.mathnet.ru/eng/rm/v66/i4/p103
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Statistics & downloads:
    Abstract page:781
    Russian version PDF:269
    English version PDF:20
    References:92
    First page:30
     
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