A Cordes framework for stationary Fokker--Planck--Kolmogorov equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917214617075712 |
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| author | Sprekeler, Timo |
| author_facet | Sprekeler, Timo |
| contents | We first review the Cordes condition for nondivergence-form differential operators through the lens of Campanato's theory of near operators. We then survey a recently proposed Cordes framework that guarantees the existence and uniqueness of $L^2$ solutions to stationary Fokker--Planck--Kolmogorov equations subject to periodic boundary conditions, and that allows for the construction of a simple finite element method for its numerical approximation. Finally, we propose a Cordes framework for stationary Fokker--Planck--Kolmogorov-type equations subject to a homogeneous Dirichlet boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Cordes framework for stationary Fokker--Planck--Kolmogorov equations Sprekeler, Timo Numerical Analysis 35B27, 35J15, 65N12, 65N15, 65N30 We first review the Cordes condition for nondivergence-form differential operators through the lens of Campanato's theory of near operators. We then survey a recently proposed Cordes framework that guarantees the existence and uniqueness of $L^2$ solutions to stationary Fokker--Planck--Kolmogorov equations subject to periodic boundary conditions, and that allows for the construction of a simple finite element method for its numerical approximation. Finally, we propose a Cordes framework for stationary Fokker--Planck--Kolmogorov-type equations subject to a homogeneous Dirichlet boundary condition. |
| title | A Cordes framework for stationary Fokker--Planck--Kolmogorov equations |
| topic | Numerical Analysis 35B27, 35J15, 65N12, 65N15, 65N30 |
| url | https://arxiv.org/abs/2601.14548 |