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Integration in variational inequalities on spatial grids

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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.

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Authors and Affiliations

  1. Voronezh State University, Russia

    Yu. V. Pokornyi & V. L. Pryadiev

  2. Voronezh State Pedagogical University, Russia

    I. Yu. Pokornaya

  3. Belgorod University of Consumer Cooperatives, Russia

    N. N. Ryabtseva

Authors
  1. Yu. V. Pokornyi
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  2. I. Yu. Pokornaya
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  3. V. L. Pryadiev
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  4. N. N. Ryabtseva
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Additional information

Original Russian Text © Yu. V. Pokornyi, I. Yu. Pokornaya, V. L. Pryadiev, N. N. Ryabtseva, 2007, published in Matematicheskie Zametki, 2007, Vol. 85, No. 6, pp. 904–911.

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Pokornyi, Y.V., Pokornaya, I.Y., Pryadiev, V.L. et al. Integration in variational inequalities on spatial grids. Math Notes 81, 810–816 (2007). https://doi.org/10.1134/S0001434607050288

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  • DOI: https://doi.org/10.1134/S0001434607050288

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