This article is cited in 2 papers

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

A. O. Ivanov^a, A. A. Tuzhilin^a, Lê Hông Vân<sup>b

a</sup> 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.

UDC: 517

Received: 15.09.1999

DOI: 10.4213/mzm523

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

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