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arXiv · 2601.14548

A Cordes framework for stationary Fokker--Planck--Kolmogorov equations

Timo Sprekeler
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Abstract

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.

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Timo Sprekeler. 2026-01-21. A Cordes framework for stationary Fokker--Planck--Kolmogorov equations. https://arxiv.org/abs/2601.14548

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