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

Aziz M. Embarek; Dmitry V. Shatilovich

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arXiv · 2604.17980

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

Aziz M. Embarek·Dmitry V. Shatilovich

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Abstract

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.

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Aziz M. Embarek, Dmitry V. Shatilovich. 2026-04-20. Existence theorems for nonlinear stationary Kolmogorov equations with partially degenerate diffusion matrices. https://arxiv.org/abs/2604.17980

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