@article{MakhmudovTarchanov2017,
  author    = {Makhmudov, O. I. and Tarchanov, Nikolaj Nikolaevič},
  title     = {The first mixed problem for the nonstationary Lam{\´e} system},
  series = {The Rocky Mountain journal of mathematics},
  volume    = {47},
  journal   = {The Rocky Mountain journal of mathematics},
  number    = {8},
  publisher = {Rocky Mountain Mathematics Consortium},
  address   = {Tempe},
  issn      = {0035-7596},
  doi       = {10.1216/RMJ-2017-47-8-2731},
  pages     = {2731 -- 2756},
  year      = {2017},
  abstract  = {We find an adequate interpretation of the stationary Lam'{e} operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lam'{e} system.},
  language  = {en}
}
@article{MeraTarchanov2017,
  author    = {Mera, Azal Jaafar Musa and Tarchanov, Nikolaj Nikolaevič},
  title     = {The Neumann Problem after Spencer},
  series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Matematika i fizika = Mathematics \& physics},
  volume    = {10},
  journal   = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Matematika i fizika = Mathematics \& physics},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2017-10-4-474-493},
  pages     = {474 -- 493},
  year      = {2017},
  abstract  = {When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.},
  language  = {en}
}
@article{VasilievTarchanov2017,
  author    = {Vasiliev, Sergey B. and Tarchanov, Nikolaj Nikolaevič},
  title     = {Construction of series of perfect lattices by layer superposition},
  series = {Journal of Siberian Federal University : Mathematics \& physics},
  volume    = {10},
  journal   = {Journal of Siberian Federal University : Mathematics \& physics},
  number    = {3},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2017-10-3-353-361},
  pages     = {353 -- 361},
  year      = {2017},
  abstract  = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.},
  language  = {en}
}
@article{AlSaedyTarchanov2020,
  author    = {Al-Saedy, Ammar Jaffar Muhesin and Tarchanov, Nikolaj Nikolaevič},
  title     = {A degree theory for Lagrangian boundary value problems},
  series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  volume    = {13},
  journal   = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  number    = {1},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-1-5-25},
  pages     = {5 -- 25},
  year      = {2020},
  abstract  = {We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.},
  language  = {en}
}
@article{ShlapunovTarchanov2021,
  author    = {Shlapunov, Alexander and Tarchanov, Nikolaj Nikolaevič},
  title     = {An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n},
  series = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  volume    = {18},
  journal   = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  number    = {2},
  publisher = {Institut Matematiki Imeni S. L. Soboleva},
  address   = {Novosibirsk},
  issn      = {1813-3304},
  doi       = {10.33048/semi.2021.18.108},
  pages     = {1433 -- 1466},
  year      = {2021},
  abstract  = {We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations.},
  language  = {en}
}