Abstract
We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies Hölder continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate. This permits to quantitatively prove the Intermediate Value Lemma for the full range of non-locality parameter s∈(0,1). Our results recover the results from Imbert and Silvestre, The weak Harnack inequality for the Boltzmann equation without cut-off, 2020. The paper is self-contained.
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