TY  - JOUR
A1  - Mera, Azal Jaafar Musa
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - The Neumann Problem after Spencer
JF  - Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Matematika i fizika = Mathematics & physics
N2  - 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.
KW  - elliptic complexes
KW  - manifolds with boundary
KW  - Hodge theory
KW  - Neumann problem
Y1  - 2017
U6  - https://doi.org/10.17516/1997-1397-2017-10-4-474-493
SN  - 1997-1397
SN  - 2313-6022
VL  - 10
SP  - 474
EP  - 493
PB  - Sibirskij Federalʹnyj Universitet
CY  - Krasnojarsk
ER  - 
TY  - JOUR
A1  - Makhmudov, O. I.
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - The first mixed problem for the nonstationary Lamé system
JF  - The Rocky Mountain journal of mathematics
N2  - 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.
KW  - Lame system
KW  - evolution equation
KW  - first boundary value problem
Y1  - 2018
U6  - https://doi.org/10.1216/RMJ-2017-47-8-2731
SN  - 0035-7596
SN  - 1945-3795
VL  - 47
IS  - 8
SP  - 2731
EP  - 2756
PB  - Rocky Mountain Mathematics Consortium
CY  - Tempe
ER  - 
TY  - JOUR
A1  - Vasiliev, Sergey B.
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - Construction of series of perfect lattices by layer superposition
JF  - Journal of Siberian Federal University : Mathematics & physics
JF  - Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Serija Matematika i fizika = Mathematics & physics
N2  - We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.
KW  - lattice packing and covering
KW  - polyhedra and polytopes
KW  - regular figures
KW  - division of spaces
Y1  - 2017
U6  - https://doi.org/10.17516/1997-1397-2017-10-3-353-361
SN  - 1997-1397
SN  - 2313-6022
VL  - 10
IS  - 3
SP  - 353
EP  - 361
PB  - Sibirskij Federalʹnyj Universitet
CY  - Krasnojarsk
ER  - 
TY  - JOUR
A1  - Shlapunov, Alexander
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n
JF  - Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija
N2  - 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.
KW  - Navier-Stokes equations
KW  - de Rham complex
KW  - open mapping theorem
Y1  - 2021
U6  - https://doi.org/10.33048/semi.2021.18.108
SN  - 1813-3304
VL  - 18
IS  - 2
SP  - 1433
EP  - 1466
PB  - Institut Matematiki Imeni S. L. Soboleva
CY  - Novosibirsk
ER  - 
TY  - JOUR
A1  - Al-Saedy, Ammar Jaffar Muhesin
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - A degree theory for Lagrangian boundary value problems
JF  - Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics & physics
N2  - 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.
N2  - Мы изучаем те нелинейные уравнения с частными производными, которые возникают как уравнения Эйлера-Лагранжа вариационных задач. Определяя слабые граничные значения решений таких уравнений, мы инициируем теорию лагранжевых краевых задач в функциональных пространствах подходящей гладкости. Мы также анализируем, применяется ли современная концепция степени отображения к лагранжевым проблемам.
KW  - nonlinear equations
KW  - Lagrangian system
KW  - weak boundary values
KW  - quasilinear Fredholm operators
KW  - mapping degree
Y1  - 2020
U6  - https://doi.org/10.17516/1997-1397-2020-13-1-5-25
SN  - 1997-1397
SN  - 2313-6022
VL  - 13
IS  - 1
SP  - 5
EP  - 25
PB  - Sibirskij Federalʹnyj Universitet
CY  - Krasnojarsk
ER  -