Geodesic
Integration in Variational Inequalities on Spatial Grids
Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 904-911

Voir la notice de l'article provenant de la source Math-Net.Ru

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, Jacobi theorem on the second variation, Stieltjes integral, Banach space, Euler–Lagrange theorem.
Mots-clés : spatial grid 
@article{MZM_2007_81_6_a8,
     author = {Yu. V. Pokornyi and I. Yu. Pokornaya and V. L. Pryadiev and N. N. Ryabtseva},
     title = {Integration in {Variational} {Inequalities} on {Spatial} {Grids}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {904--911},
     publisher = {mathdoc},
     volume = {81},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a8/}
}
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Yu. V. Pokornyi; I. Yu. Pokornaya; V. L. Pryadiev; N. N. Ryabtseva. Integration in Variational Inequalities on Spatial Grids. Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 904-911. http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a8/