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Gradient Riesz potential estimates for a general class of measure data quasilinear systems

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arxiv 2307.15525 v1 pith:CPU5GFQG submitted 2023-07-28 math.AP

Iwona Chlebicka , Minhyun Kim , Marvin Weidner This is my paper · ORCID
classification math.AP
keywords datagradientmeasuresolutionsestimatespotentialregularityriesz
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We study the gradient regularity of solutions to measure data elliptic systems with Uhlenbeck-type structure and Orlicz growth. For any bounded Borel measure, pointwise estimates for the gradient of solutions are provided in terms of the truncated Riesz potential. This allows us to show a precise transfer of regularity from data to solutions on various scales.

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  1. Gradient estimates for nonlinear kinetic Fokker-Planck equations

    math.AP 2025-02 conditional novelty 8.0 of 10

    For nonlinear kinetic Fokker-Planck equations, the velocity gradient is controlled pointwise by kinetic Riesz potentials of the data, yielding new Hölder, BMO, and Calderón-Zygmund regularity criteria.

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