collaborators

14 papers

math.AP2026

Lions' Maximal Regularity Problem for Divergence-Form Differential Operators: Failure at the -Hölder Endpoint

Lukas Niebel

In this work we give a counterexample to maximal -regularity in Lions' problem for divergence-form differential operators. On a bounded interval, we construct a bound…

math.AP2026

An autonomous Lipschitz fast dynamo on the three-torus

Lukas Niebel

We construct a single real-valued, divergence-free, time-independent velocity field that is a fast dynamo for the kinematic…

math.AP2026

Sharp kinetic trace theory

Lukas Niebel, Lisa Valentini

We establish sharp kinetic trace estimates and counterexamples across several velocity models. For half-space position domains, without any common bound on velocity support, we pro…

math.AP2026

Transfer of regularity by kinetic mollification along critical trajectories

Lukas Niebel

We give a trajectory-based proof of transfer-of-regularity estimates à la Bouchut-Hörmander for kinetic equations at the weak scale of local diffusion. The proof is based on kinet…

math.AP2026

On the kinetic -Laplace equation with nonlocal diffusion

Lukas Niebel

We study two nonlocal versions of the kinetic -Laplace equation: a Gagliardo-type model defined through differences and a Bessel-type model defined via Fourier multiplication. U…

math.AP2026

Nonlinear Kinetic Diffusion Equations with -Growth

Helge Dietert, Lukas Niebel, Rico Zacher

We establish the local boundedness of (sub-)solutions to nonlinear kinetic diffusion equations with -growth, where the kinetic p-Laplace equation is a prototypical example. A ke…