Zobrazeno 1 - 10
of 132
pro vyhledávání: '"Filonov, N."'
Autor:
Filonov, N. D., Krymskii, S. T.
The equation $- \Delta u + V u = 0$ in the cylinder $\mathbb{R} \times (0,2\pi)^d$ with periodic boundary conditions is considered. The potential $V$ is assumed to be bounded, and both functions $u$ and $V$ are assumed to be real-valued. It is shown
Externí odkaz:
http://arxiv.org/abs/2311.14491
Autor:
Filonov, N.
Denote by $N_{\cal N} (\Omega,\lambda)$ the counting function of the spectrum of the Neumann problem in the domain $\Omega$ on the plane. G. P\'olya conjectured that $N_{\cal N} (\Omega,\lambda) \ge (4\pi)^{-1} |\Omega| \lambda$. We prove that for co
Externí odkaz:
http://arxiv.org/abs/2309.01432
Autor:
Filonov, N.
In 1954, G. Polya conjectured that the counting function $N(\Omega,\Lambda)$ of the eigenvalues of the Laplace operator of the Dirichlet (resp. Neumann) boundary value problem in a bounded set $\Omega\subset R^d$ is lesser (resp. greater) than $(2\pi
Externí odkaz:
http://arxiv.org/abs/2208.03463
Autor:
Filonov, N.
The Maxwell operator in a 3D cylinder is considered. The coefficients are assumed to be scalar functions depending on the longitudinal variable only. Such operator is represented as a sum of countable set of matrix differential operators of first ord
Externí odkaz:
http://arxiv.org/abs/2012.01034
Akademický článek
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Akademický článek
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Autor:
Filonov, N., Prokhorov, A.
Publikováno v:
Algebra i Analiz, tom 29 (2017), nomer 6; St. Petersburg Math. J. 29 (2018), 997-1006
In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is
Externí odkaz:
http://arxiv.org/abs/1801.10440
Autor:
Filonov, N.
The dyadic problem $\dot u_n + \lambda^{2n} u_n - \lambda^{\beta n} u_{n-1}^2 + \lambda^{\beta(n+1)} u_n u_{n+1} = 0$ with "smooth" initial data is considered. The uniqueness of the Leray-Hopf solution is proved.
Externí odkaz:
http://arxiv.org/abs/1506.07480
Autor:
Filonov, N., Prokhorov, A.
In this paper the "strong" Maxwell operator defined on fields from the Sobolev space $W_2^1$, and the "weak" Maxwell operator defined on the natural domain are considered. It is shown that in a convex domain, and, more generally, in a domain, which i
Externí odkaz:
http://arxiv.org/abs/1501.07081
Autor:
Filonov, N. D., Khodunov, P. A.
Publikováno v:
Journal of Mathematical Sciences; Aug2024, Vol. 283 Issue 5, p816-824, 9p
