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<p>We obtain Sobolev regularity estimates for solutions of non-local parabolic equations with locally unbounded drift satisfying some minimal assumptions. These results yield Krylov bound for the corresponding Feller stable process as well as some a priori regularity estimates on solutions of McKean–Vlasov equations. A key element of our arguments is a parabolic operator norm inequality that we prove using some ideas of Adams and Krylov.</p>

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Non-local Parabolic Equations with Singular (Morrey) Time-Inhomogeneous Drift

  • 期刊论文

  • 发表日期：

    2025年5月23日

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  • D. Kinzebulatov

摘要

We obtain Sobolev regularity estimates for solutions of non-local parabolic equations with locally unbounded drift satisfying some minimal assumptions. These results yield Krylov bound for the corresponding Feller stable process as well as some a priori regularity estimates on solutions of McKean–Vlasov equations. A key element of our arguments is a parabolic operator norm inequality that we prove using some ideas of Adams and Krylov.