Existence theorems for nonlinear stationary Kolmogorov equations with partially degenerate diffusion matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908979894943744 |
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| author | Embarek, Aziz M. Shatilovich, Dmitry V. |
| author_facet | Embarek, Aziz M. Shatilovich, Dmitry V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17980 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence theorems for nonlinear stationary Kolmogorov equations with partially degenerate diffusion matrices Embarek, Aziz M. Shatilovich, Dmitry V. Analysis of PDEs 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. |
| title | Existence theorems for nonlinear stationary Kolmogorov equations with partially degenerate diffusion matrices |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.17980 |