arXiv subjects

Dmitry V. Shatilovich

Publications and source records attributed to Dmitry V. Shatilovich.

2 recordsLinked to original sources

arXiv2026

Existence theorems for nonlinear stationary Kolmogorov equations with partially degenerate diffusion matrices

We study nonlinear stationary Kolmogorov equations with degenerate diffusion matrices and discontinuous coefficients. The existence of a solution is proved. We propose a new approach based on an integral condition with Lyapunov functions and a regularity of projections of solutions in the partially degenerate case. Examples are given to illustrate the results.

math.AP↗

arXiv2026

Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria

We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Figalli-Trevisan superposition principle, the method of doubling variables and a~priory estimates with Lyapunov functions.

math.AP↗