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De Giorgi-Nash-Moser theory for kinetic equations with nonlocal diffusions
We extend the De Giorgi--Nash--Moser theory to nonlocal hypoelliptic equations arising in kinetic theory as linearized models for the non-cutoff Boltzmann equation. Assuming that the nonlocal tail in velocity of weak solutions belongs locally to $L^p_{t,x}$ for some $p>N_{d}/(2s)$, where $N_{d}$ is
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