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Russian Academy of Sciences. Izvestiya Mathematics, 1995, Volume 45, Issue 3, Pages 433–476
DOI: https://doi.org/10.1070/IM1995v045n03ABEH001674 (Mi im522) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the theory of degenerate quadratic forms in the classical calculus of variations

A. V. Arutyunov
English version PDF (2258 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM1995v045n03ABEH001674
Abstract: This paper investigates the property of having definite sign for a quadratic form in the calculus of variations that does not satisfy the strong Legendre condition. New necessary conditions (the condition $\mathscr A$) of pointwise nature are obtained for the index of a form to be finite. Under the assumption of the strong condition $\mathscr A$ a formula is obtained for the index of a form.
Received: 24.03.1993
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1994, Volume 58, Issue 6, Pages 3–50
Bibliographic databases:
UDC: 519.3
MSC: Primary 49N99; Secondary 58E30, 49L05, 15A63
Language: English
Original paper language: Russian
Citation: A. V. Arutyunov, “On the theory of degenerate quadratic forms in the classical calculus of variations”, Izv. RAN. Ser. Mat., 58:6 (1994), 3–50; Russian Acad. Sci. Izv. Math., 45:3 (1995), 433–476
Citation in format AMSBIB
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\by A.~V.~Arutyunov
\paper On the theory of degenerate quadratic forms in the classical calculus of variations
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 6
\pages 3--50
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1317207}
\zmath{https://zbmath.org/?q=an:0853.49015}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 45
\issue 3
\pages 433--476
\crossref{https://doi.org/10.1070/IM1995v045n03ABEH001674}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TW91000001}
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  • https://doi.org/10.1070/IM1995v045n03ABEH001674
  • https://www.mathnet.ru/eng/im/v58/i6/p3
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:505
    Russian version PDF:277
    English version PDF:29
    References:68
    First page:1
     
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