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arXiv · 2405.08652

Non-local parabolic equations with singular (Morrey) time-inhomogeneous drift

Damir Kinzebulatov
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Abstract

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.

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Damir Kinzebulatov. 2024-05-14. Non-local parabolic equations with singular (Morrey) time-inhomogeneous drift. https://arxiv.org/abs/2405.08652

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