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math.AP2026
Existence and upper bounds of fundamental solutions to kinetic equations with rough non-local diffusion
Pascal Auscher, Lukas Niebel
We study the fundamental solution operators associated to Kolmogorov equations with symmetric non-local diffusion with rough kernels. We prove that these operators are induced by m…
math.AP2026
Existence and uniqueness of weak solutions to quasilinear PDEs with critical data
Pascal Auscher, Sebastian Bechtel
We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreov…
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…