preprint
Inserted: 14 oct 2024
Last Updated: 14 oct 2024
Year: 2023
Abstract:
We investigate local properties of weak solutions to the following wide class of kinetic equations, \[ (\partial_t \,+\, v\cdot\nabla_x) f \, = \, \mathcal{L}_v f. \] Above, the diffusion term $\mathcal{L}_v$ is an integro-differential operator whose nonnegative kernel is of differentiability order $s \in (0,1)$ and integrability oredr $p \in (2,\infty)$, having merely measurable coefficients. In particular, we provide explicit interpolative $L^\infty$-$L^2$ estimates for weak subsolutions.
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