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Mat. Zametki, 2001, Volume 69, Issue 4, Pages 566–580 (Mi mz523)  

This article is cited in 2 scientific papers (total in 2 papers)

Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality

A. O. Ivanova, A. A. Tuzhilina, Lê Hông Vânb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b M. V. Lomonosov Moscow State University

Abstract: We single out the class of so-called quasiregular Lagrangians, which have singularities on the zero section of the cotangent bundle to the manifold on which extremal networks are considered. A criterion for a network to be extremal is proved for such Lagrangians: the Euler–Lagrange equations must be satisfied on each edge, and some matching conditions must be valid at the vertices.

DOI: https://doi.org/10.4213/mzm523

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English version:
Mathematical Notes, 2001, 69:4, 514–526

Bibliographic databases:

UDC: 517
Received: 15.09.1999

Citation: A. O. Ivanov, A. A. Tuzhilin, Lê Hông Vân, “Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality”, Mat. Zametki, 69:4 (2001), 566–580; Math. Notes, 69:4 (2001), 514–526

Citation in format AMSBIB
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\jour Math. Notes
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\pages 514--526
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. O. Ivanov, A. A. Tuzhilin, “Branching geodesics in normed spaces”, Izv. Math., 66:5 (2002), 905–948  mathnet  crossref  crossref  mathscinet  zmath
    2. Ivanov A.O. Tuzhilin A.A., “Minimal Networks: a Review”, Advances in Dynamical Systems and Control, Studies in Systems Decision and Control, 69, ed. Sadovnichiy V. Zgurovsky M., Springer Int Publishing Ag, 2016, 43–80  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математические заметки Mathematical Notes
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