Non-local parabolic equations with singular (Morrey) time-inhomogeneous drift
Analysis of PDEs
2024-05-15 v1 Probability
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.
Keywords
Cite
@article{arxiv.2405.08652,
title = {Non-local parabolic equations with singular (Morrey) time-inhomogeneous drift},
author = {Damir Kinzebulatov},
journal= {arXiv preprint arXiv:2405.08652},
year = {2024}
}