@unpublished{SchulzeShlapunovTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Green integrals on manifolds with cracks},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25777},
  year      = {2000},
  abstract  = {We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D.},
  language  = {en}
}
@article{ShlapunovTarchanov2022,
  author    = {Shlapunov, Alexander A. and Tarchanov, Nikolaj Nikolaevič},
  title     = {Inverse image of precompact sets and regular solutions to the Navier-Stokes equations},
  series = {Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki},
  volume    = {32},
  journal   = {Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki},
  number    = {2},
  publisher = {Udmurtskij gosudarstvennyj universitet},
  address   = {Iževsk},
  issn      = {1994-9197},
  doi       = {10.35634/vm220208},
  pages     = {278 -- 297},
  year      = {2022},
  abstract  = {We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting. We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N. Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r.},
  language  = {en}
}