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A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation

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arxiv 2407.08785 v1 pith:UZUPQTPY submitted 2024-07-11 math.AP

Christopher Henderson , Giacomo Lucertini , Weinan Wang This is my paper · ORCID
classification math.AP
keywords kineticboundaryinequalityabsorbingbehaviorfokker-planckhalf-spacenash
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In this paper, we prove a kinetic Nash type inequality and adapt it to a new functional inequality for functions in a kinetic Sobolev space with absorbing boundary conditions on the half-space. As an application, we address the boundary behavior of the kinetic Fokker-Planck equations in the half-space. Our main result is the sharp regularity of the solution at the absorbing boundary and grazing set.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sharp kinetic trace theory

    math.AP 2026-07 accept novelty 8.0 of 10

    Natural kinetic traces hold on half-spaces unrestricted, fail for unrestricted Gaussian when p<2 on every bounded C^{1,1} domain, and for bounded velocities are sharp exactly at boundary regularity α_p=1/(p+1).

  2. Kinetic Fokker-Planck equations with Maxwell boundary conditions

    math.AP 2026-07 conditional novelty 8.0 of 10

    For every α∈(0,1), solutions to the kinetic Fokker-Planck equation with Maxwell boundary conditions are C^{3/π·arccos(α/2)−1} up to the grazing set, and this exponent is optimal.

  3. Optimal regularity for kinetic Fokker-Planck equations in domains

    math.AP 2025-05 conditional novelty 8.0 of 10

    Solutions to kinetic Fokker-Planck equations with specular reflection are C^{4,1} in the kinetic Hölder sense up to the grazing set, and this regularity is optimal.

  4. Sharp boundary regularity properties for hypoelliptic kinetic equations

    math.AP 2025-09 conditional novelty 7.0 of 10

    The paper establishes sharp Hölder, gradient, and exponential-vanishing boundary estimates, including optimal C^{1/2} regularity at grazing boundaries, for kinetic Fokker-Planck equations with rough or regular coefficients.

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