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Sharp boundary regularity properties for hypoelliptic kinetic equations

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arxiv 2509.02536 v1 pith:SCF5MYC2 submitted 2025-09-02 math.AP

Yuzhe Zhu This is my paper · ORCID
classification math.AP
keywords boundaryboundariesequationsregularitycoefficientsgrazinghypoellipticincoming
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We establish sharp boundary regularity results for solutions to kinetic Fokker-Planck equations under prescribed inflow boundary conditions, providing precise quantification of the boundary hypoelliptic regularization effect. For equations with rough coefficients, we characterize the behaviours for solutions on grazing and incoming boundaries. In particular, in the absence of influxes and sources, an explicit exponential infinite-order vanishing estimate is derived near incoming boundaries. When the coefficients are regular, we obtained the optimal H\"older regularity on grazing boundaries and general Schauder-type estimates away from them.

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  1. 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.

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