A trajectory-based approach yields sharp, scale-invariant transfer-of-regularity estimates for kinetic equations at the local diffusion scale without Fourier computations or the fundamental solution.
Critical trajectories in kinetic geometry, 2025
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Derives representation formulas and scale-invariant kinetic Gagliardo-Nirenberg inequalities for two nonlocal kinetic p-Laplace models, yielding gain-of-integrability for weak solutions.
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A new proof of the transfer of regularity for kinetic equations
A trajectory-based approach yields sharp, scale-invariant transfer-of-regularity estimates for kinetic equations at the local diffusion scale without Fourier computations or the fundamental solution.
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On the kinetic $p$-Laplace equation with nonlocal diffusion
Derives representation formulas and scale-invariant kinetic Gagliardo-Nirenberg inequalities for two nonlocal kinetic p-Laplace models, yielding gain-of-integrability for weak solutions.