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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
On Hardy-Littlewood-Sobolev estimates for degenerate Laplacians
Pascal Auscher, Khalid Baadi
We establish norm inequalities for fractional powers of degenerate Laplacians, with degeneracy being determined by weights in the Muckenhoupt class , accompanied…
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…