Tuesday, March 18, 2025 - 14:40 in V2-205
Nonlocal theory for fractional kinetic equations
A talk in the Nonlocal Equations: Analysis and Numerics series by
Mirco Piccinini from Pisa
| Abstract: |
We extend the De Giorgi-Nash-Moser theory to a class of nonlocal
hypoelliptic equations naturally arising in kinetic theory, which combine a
first-order transport term with an elliptic operator involving fractional
derivatives along only part of the coordinates. Under sufficient integrability
along the transport variables on the nonlocal tail, we prove the first local
supremum estimate for this class of equations. Then, we establish the first
full Harnack inequality for solutions to kinetic integral equations under
the aforementioned tail summability assumption, which appears in clear
accordance with the very recent counterexample by Kassmann and Weidner
(Adv. in Math. 2024). This is based on series of papaers by F. Anceschi,
M. Kassmann, A. Loher, G. Palatucci, M. Weidner and myself.
Within the CRC this talk is associated to the project(s): A7 |
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