P. Vilkov

activity

20222025

collaborators

3 papers

math.AP2025

On approximation theorems for solutions to strongly parabolic systems in anisotropic Sobolev spaces

Alexander Shlapunov, Pavel Vilkov

We investigate the problem on Runge pairs for Sobolev solutions of strongly uniformly parabolic systems in non-cylindrical domains of a special kind. We prove that if the coefficie…

math.AP2023

On Runge type theorems for solutions to strongly uniformly parabolic operators

P. Yu. Vilkov, A. A. Shlapunov

Let $G_{1}, G_{2}$ be domains in $R^{n + 1}$ , $n \geq 2$ , such that $G_{1} \subset G_{2}$ and the domain $G_{1}$ have rather regular boundary. We investigate the problem of approxim…

math.AP2022

Approximation of solutions to parabolic Lamé type operators in cylinder domains and Carleman's formulas for them

Pavel Vilkov, Il'ya Kurilenko, Alexander Shlapunov

Let $s \in N$ , $T_{1}, T_{2} \in R$ , $T_{1} < T_{2}$ , and let $Ω, ω$ be bounded domains in $R^{n}$ , $n \geq 1$ such that $ω \subset Ω$ and the complement $Ω\setminu…