Long-time contractivity estimates for kinetic Kolmogorov-Fokker-Planck equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917011144048640 |
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| author | Forcillo, Nicolò Porretta, Alessio |
| author_facet | Forcillo, Nicolò Porretta, Alessio |
| contents | We prove long-time contractivity estimates and exponential rates of convergence to equilibrium for solutions of hypoelliptic diffusion equations, which include the well-known Kolmogorov equation and similar kinetic Fokker-Planck equations in $\R^d$. Compared to the existing literature, our proof exploits a different approach, elementary and self-contained, based on oscillation estimates for the adjoint problem. We first prove contractivity in Wasserstein distances through doubling variables (coupling) methods. Next, we upgrade the estimate to weighted $L^1$-(or total variation) norms, thanks to short-time hypocoercivity gradient estimates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_11901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-time contractivity estimates for kinetic Kolmogorov-Fokker-Planck equations Forcillo, Nicolò Porretta, Alessio Analysis of PDEs 35Q84, 35K65, 35H10 We prove long-time contractivity estimates and exponential rates of convergence to equilibrium for solutions of hypoelliptic diffusion equations, which include the well-known Kolmogorov equation and similar kinetic Fokker-Planck equations in $\R^d$. Compared to the existing literature, our proof exploits a different approach, elementary and self-contained, based on oscillation estimates for the adjoint problem. We first prove contractivity in Wasserstein distances through doubling variables (coupling) methods. Next, we upgrade the estimate to weighted $L^1$-(or total variation) norms, thanks to short-time hypocoercivity gradient estimates. |
| title | Long-time contractivity estimates for kinetic Kolmogorov-Fokker-Planck equations |
| topic | Analysis of PDEs 35Q84, 35K65, 35H10 |
| url | https://arxiv.org/abs/2510.11901 |