English

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}
}