Geodesic
Topological characteristics of non-smooth functionals
Izvestiya. Mathematics , Tome 62 (1998) no. 5, pp. 969-984

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We establish infinite-dimensional variants of the Poincare–Hopf theorem for many-valued vector fields generated by operators of monotonic type. We suggest conditions for the stabilization of the homology groups of closed subsets of a Banach space when approximated by finite-dimensional sections. Emphasis is given to the study of topological characteristics of Lebesgue sets of Lipschitz functionals defined on a closed convex subset of a reflexive space. 
@article{IM2_1998_62_5_a4,
     author = {V. S. Klimov},
     title = {Topological characteristics of non-smooth functionals},
     journal = {Izvestiya. Mathematics },
     pages = {969--984},
     publisher = {mathdoc},
     volume = {62},
     number = {5},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_5_a4/}
}
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V. S. Klimov. Topological characteristics of non-smooth functionals. Izvestiya. Mathematics , Tome 62 (1998) no. 5, pp. 969-984. http://geodesic.mathdoc.fr/item/IM2_1998_62_5_a4/