Quantitative stability estimates for Fokker-Planck equations
arXiv:1701.00566 · doi:10.1016/j.matpur.2018.08.003
Abstract
We consider the Fokker--Planck equations with irregular coefficients. Two different cases are treated: in the degenerate case, the coefficients are assumed to be weakly differentiable, while in the non-degenerate case the drift satisfies only the Ladyzhenskaya--Prodi--Serrin condition. Using Trevisan's superposition principle which represents the solution as the marginal of the solution to the martingale problem of the diffusion operator, we establish quantitative stability estimates for the solutions of Fokker--Planck equations.
35 pages
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Cited by in corpus (5)
- On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity
- Weak and parabolic solutions of advection-diffusion equations with rough velocity field
- Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels
- A regularity result for the Fokker-Planck equation with non-smooth drift and diffusion
- Kantorovich-Rubinstein Distance and Approximation for Non-local Fokker-Planck Equations