8 citations · 11 across the 11 of their papers we have counts for
12 papers
On the inequality for the eigenvalues of the Laplace operator
N. Filonov
In 1952, Pólya proved the inequality for the eigenvalues of Dirichlet and Neumann problems in domain , . We show that if $d\…
On the Pólya conjecture for circular sectors and for balls
N. Filonov
In 1954, G. Polya conjectured that the counting function of the eigenvalues of the Laplace operator of the Dirichlet (resp. Neumann) boundary value problem in a bounded se…
Maxwell operator in a cylinder. Separation of variables
N. Filonov
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 a…
On the Pólya conjecture for the Neumann problem in tiling sets
Nikolai Filonov
In 1954, G. Pólya conjectured that the counting function of the eigenvalues of the Laplace operator of Dirichlet (resp. Neumann) boundary value problem in a bounded set $Ω\subset{\…
Non-uniqueness of Leray-Hopf solutions for a dyadic mode
Nikolai Filonov, Pavel Khodunov
The dyadic model , , is considered. It is shown that in the case of non-trivial right hand side the s…
The Maxwell operator with periodic coefficients in a cylinder
N. Filonov, A. Prokhorov
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…