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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

A Liouville theorem for the two-dimensional stationary hypodissipative Navier--Stokes system

Nicola De Nitti, Lukas Niebel, Jiaqi Yang

We study the two-dimensional stationary incompressible Navier--Stokes equations on with fractional dissipation . In the full range , we prove tha…

math.AP2026

Spherical rigidity for an exterior overdetermined problem with Neumann data prescribed by mean curvature

Lukas Niebel

We study an overdetermined elliptic free boundary problem for exterior domains in , , introduced by F. Morabito [Comm. PDE 46 (2021), 1137-1161]. The overdet…

math.AP2026

Kinetic Sobolev Spaces

Pascal Auscher, Lukas Niebel

We define and study homogeneous kinetic Sobolev spaces adapted to the Kolmogorov equation. We consider both local and non-local diffusion. The spaces are built from the Lebesgue sp…

math.AP2025

Nash's bound for the Kolmogorov equation

Helge Dietert, Lukas Niebel

We prove Nash's bound for the Kolmogorov equation with rough coefficients. Our proof is inspired by the treatment of the parabolic problem by Nash (1958) and Fabes and Stroock…

math.AP2025

Critical trajectories in kinetic geometry

Helge Dietert, Clément Mouhot, Lukas Niebel +1

We construct critical trajectories in kinetic geometry, i.e. curves in that are: tangential to the vector fields and , co…