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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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This publication is cited in the following articles:
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A. O. Ivanov, A. A. Tuzhilin, “Branching geodesics in normed spaces”, Izv. Math., 66:5 (2002), 905–948
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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
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