Lukas Niebel

P. Auscher, C. Imbert and L. Niebel
Weak solutions to Kolmogorov-Fokker-Planck equations: Regularity, existence and uniqueness
HAL/arXiv (2024).
[HAL][arXiv]

P. Auscher, C. Imbert and L. Niebel
Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: Existence, uniqueness, upper estimates
HAL/Arxiv (2024).
[HAL][arXiv]

L. Niebel and R. Zacher
On a kinetic Poincaré inequality and beyond
ArXiv (2022).
[arXiv]

L. Niebel and R. Zacher
A trajectorial interpretation of Moser's proof of the Harnack inequality
To appear in Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2023).
[arXiv]
L. Niebel and R. Zacher
Kinetic maximal \(L^p \)-regularity with temporal weights and application to quasilinear kinetic diffusion equations
In Journal of Differential Equations 307, 29 — 82 (2022).
[Journal] [arXiv]
L. Niebel
Kinetic maximal \(L^p_\mu(L^p) \)-regularity for the fractional Kolmogorov equation with variable density
In Nonlinear Analysis 214 (2022).
[Journal] [arXiv]
L. Niebel and R. Zacher
Kinetic maximal \(L^2 \)-regularity for the (fractional) Kolmogorov equation
In Journal of Evolution Equations 21, 3585 — 3612 (2021).
[Journal] [arXiv]

L. Niebel
On analytic aspects of kinetic partial differential equations
PhD Thesis, June 2023
[Summary] [pdf]
L. Niebel
Kolmogorov Equations - Well-Posedness, Regularity, Asymptotics and Harnack inequalites
Master Thesis, March 2019
[pdf]
L. Niebel
Long-time behavior of Markov chains by discrete functional inequalities and entropic Ricci curvature
in german
Bachelor Thesis, 2018
[pdf]

L. Niebel
Fourier transformation as the Gelfand transformation on \( L^1(\mathbb{R}) \)
in german
Seminar presentation, June 2017
[pdf]