Lukas Niebel
Mathematician
Department of Mathematics
ETH Zürich
niebel.math@gmail.com
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Preprints
- A. Loher, C. Mooney, C. Mouhot, L. Niebel, L. Silvestre and Y. Zhu
An Aleksandrov estimate for kinetic equations with rough coefficients
arXiv (2026).
[arXiv]
- P. Auscher and L. Niebel
Existence and upper bounds of fundamental solutions to kinetic equations with rough non-local diffusion
arXiv (2026).
[arXiv]
- B. Gebhard, L. Niebel and C. Seis
On Leonardo da Vinci's paradox
arXiv (2026).
[arXiv]
- N. De Nitti, L. Niebel and J. Yang
A Liouville theorem for the two-dimensional stationary hypodissipative Navier–Stokes system
arXiv (2026).
[arXiv]
- L. Niebel
Lions' maximal regularity problem for divergence-form differential operators: Failure at the \(\frac{1}{2}\)-Hölder endpoint
arXiv (2026).
[arXiv]
- L. Niebel
A fast dynamo with zero topological entropy
arXiv (2026).
[arXiv]
- L. Niebel and L. Valentini
Sharp kinetic trace theory
arXiv (2026).
[arXiv]
- L. Niebel
On the kinetic \(p\)-Laplace equation with nonlocal diffusion
arXiv (2026).
[arXiv]
- H. Dietert, L. Niebel, and R. Zacher
Nonlinear kinetic diffusion equations with \(p\)-growth
arXiv/HAL (2026).
[arXiv] [HAL]
- L. Niebel
Transfer of regularity by kinetic mollification along critical trajectories
arXiv (2026).
[arXiv]
- L. Niebel
Spherical rigidity for an exterior overdetermined problem with Neumann data prescribed by mean curvature
arXiv (2026).
[arXiv]
- H. Dietert and L. Niebel
Nash's \( G \) bound for the Kolmogorov equation
arXiv (2025).
[arXiv]
- H. Dietert, C. Mouhot, L. Niebel and R. Zacher
Critical trajectories in kinetic geometry
arXiv (2025).
[arXiv]
Publications
- L. Niebel
Global rigidity of two-dimensional bubbles
To appear in Archive for Rational Mechanics and Analysis (2026).
[arXiv] - D. Meyer, L. Niebel and C. Seis
Steady bubbles and drops in inviscid fluids
In Calculus of Variations and Partial Differential Equations 64, 299 (2025).
[Journal] [arXiv] - L. Niebel and R. Zacher
A trajectorial interpretation of Moser's proof of the Harnack inequality
In Annali Scuola Normale Superiore Di Pisa - Classe Di Scienze, 26(2) (2025).
[Journal] [arXiv] - L. Niebel and R. Zacher
On a kinetic Poincaré inequality and beyond
In Journal of Functional Analysis 289, 11 (2025).
[Journal] [arXiv] - P. Auscher, C. Imbert and L. Niebel
Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: Existence, uniqueness, upper estimates
In SIAM Journal on Mathematical Analysis 57 No. 2, 2114 — 2137 (2025).
[Journal] [arXiv] [HAL] - L. Niebel and R. Zacher
Kinetic maximal \(\mathrm{L}^p \)-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 \(\mathrm{L}^p_\mu(\mathrm{L}^p) \)-regularity for the fractional Kolmogorov equation with variable density
In Nonlinear Analysis 214 (2022).
[Journal] [arXiv] - L. Niebel and R. Zacher
Kinetic maximal \(\mathrm{L}^2 \)-regularity for the (fractional) Kolmogorov equation
In Journal of Evolution Equations 21, 3585 — 3612 (2021).
[Journal] [arXiv]
Theses
- 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]
Miscellaneous
- L. Niebel
Fourier transformation as the Gelfand transformation on \( \mathrm{L}^1(\mathbb{R}) \)
in german
Seminar presentation, June 2017
[pdf]
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