21 citations · 46 across the 8 of their papers we have counts for
9 papers
Inequalities between Dirichlet and Neumann eigenvalues in large dimensions
N. Filonov
Let be a bounded domain in . Denote by (resp. ) the eigenvalues of the Laplace operator in with Dirichlet (resp. Neumann) boundary conditions. Denote by $Ψ=…
On spectral bands of discrete periodic operators
Nikolay Filonov, Ilya Kachkovskiy
We consider discrete periodic operator on with respect to lattices of full rank. We describe the class of lattices for which the operator ma…
Pólya's conjecture for Euclidean balls
Nikolay Filonov, Michael Levitin, Iosif Polterovich +1
The celebrated Pólya's conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can…
On some properties of weak solutions to elliptic equations with divergence-free drifts
Nikolay Filonov, Timofey Shilkin
We discuss the local properties of weak solutions to the equation . The corresponding theory is well-known in the case , where is the dimensio…
On the structure of band edges of 2d periodic elliptic operators
Nikolay Filonov, Ilya Kachkovskiy
For a wide class of 2D periodic elliptic operators, we show that the global extrema of all spectral band functions are isolated.
On the regularity of solutions to the equation - Δu + b \nabla u = 0
N. Filonov
We consider the equation - Δu + b \nabla u = 0. The dependence of the local regularity of a solution on the properties of the coefficient b is investigated.