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Matematicheskie Zametki, 2007, Volume 81, Issue 6, Pages 904–911
DOI: https://doi.org/10.4213/mzm3740 (Mi mzm3740) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Integration in Variational Inequalities on Spatial Grids

Yu. V. Pokornyia, I. Yu. Pokornayab, V. L. Pryadieva, N. N. Ryabtsevac

a Voronezh State University
b Voronezh State Pedagogical University
c Belgorod University of Consumer's Cooperation
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DOI: https://doi.org/10.4213/mzm3740
Abstract: We prove an analog of the classical Jacobi theorem concerning the positive definiteness of the second variation for a functional defined on functions of branching argument belonging to a spatial grid (a geometric graph). The singularities of the corresponding analog of the Jacobi equation (and of the Euler equation) are generated by the procedure of integration by parts, which leads to differentiation with respect to measures glued (joined) together.
Keywords: variational problem, integration, geometric graphs, spatial grid, Jacobi theorem on the second variation, Stieltjes integral, Banach space, Euler–Lagrange theorem.
Received: 21.12.2004
Revised: 17.04.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 6, Pages 810–816
DOI: https://doi.org/10.1134/S0001434607050288
Bibliographic databases:
UDC: 517.927
Language: Russian
Citation: Yu. V. Pokornyi, I. Yu. Pokornaya, V. L. Pryadiev, N. N. Ryabtseva, “Integration in Variational Inequalities on Spatial Grids”, Mat. Zametki, 81:6 (2007), 904–911; Math. Notes, 81:6 (2007), 810–816
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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