Seminar series
Date
Thu, 12 May 2022
Time
12:00 -
13:00
Location
L5
Speaker
Amélie Loher
Organisation
University of Cambridge
We derive quantitatively the weak and strong Harnack inequality for kinetic Fokker--Planck type equations with a non-local diffusion operator for the full range of the non-locality exponents in (0,1). This implies Hölder continuity. We give novel proofs on the boundedness of the bilinear form associated to the non-local operator and on the construction of a geometric covering accounting for the non-locality to obtain the Harnack inequalities. Our results apply to the inhomogeneous Boltzmann equation in the non-cutoff case.