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arXiv · 2203.16137

Quantitative De Giorgi methods in kinetic theory for non-local operators

Amélie Loher
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Abstract

We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies H\"older 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 $s \in (0, 1)$. Our results recover the results from Imbert and Silvestre [22] for the inhomogeneous Boltzmann equation in the non-cutoff case. The paper is self-contained.

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Amélie Loher. 2022-03-30. Quantitative De Giorgi methods in kinetic theory for non-local operators. https://arxiv.org/abs/2203.16137

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