Calculus of Variations and Geometric Measure Theory

F. Anceschi - M. Piccinini

Boundedness estimates for nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations

created by piccinini on 14 Oct 2024

[BibTeX]

preprint

Inserted: 14 oct 2024
Last Updated: 14 oct 2024

Year: 2023

ArXiv: 2301.06334 PDF

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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