| Abstract: |
| In this talk, we focus on the study of a class of kinetic equations, whose prototype is the nonlinear Kolmogorov-Fokker-Planck equation. Through a geometrical approach, we prove a Poincar\`e inequality for weak solutions, a fundamental result for the study of the weak regularity theory and the consequent proof of a weak Harnack inequality.
The talk is based on two joint works, the first one in collaboration with Dietert, Guerand, Loher, Mouhot and Rebucci, and the second one with Guerand and Isernia. |
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