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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…
Form domination and tent space estimates for operators on the half-space
Pascal Auscher, Hedong Hou, Emiel Lorist +1
We study operators acting on functions defined on the half-space, with methods inspired by sparse domination. Using the specific link between dyadic grids on the boundary and Whitn…
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…
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…