Open Access
2023 Sharp solvability for singular SDEs
Damir Kinzebulatov, Yuliy A. Semënov
Author Affiliations +
Electron. J. Probab. 28: 1-15 (2023). DOI: 10.1214/23-EJP957


The attracting inverse-square drift provides a prototypical counterexample to solvability of singular SDEs: if the coefficient of the drift is larger than a certain critical value, then no weak solution exists. We prove a positive result on solvability of singular SDEs where this critical value is attained from below (up to strict inequality) for the entire class of form-bounded drifts. This class contains e.g. the inverse-square drift, the critical Ladyzhenskaya-Prodi-Serrin class. The proof is based on a Lp variant of De Giorgi’s method.

Funding Statement

The research of D.K. is supported by the NSERC (grant RGPIN-2017-05567).


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Damir Kinzebulatov. Yuliy A. Semënov. "Sharp solvability for singular SDEs." Electron. J. Probab. 28 1 - 15, 2023.


Received: 25 October 2021; Accepted: 3 May 2023; Published: 2023
First available in Project Euclid: 12 May 2023

MathSciNet: MR4587446
zbMATH: 07707101
Digital Object Identifier: 10.1214/23-EJP957

Primary: 35J75 , 60H10

Keywords: Parabolic equations , singular drifts , stochastic equations

Vol.28 • 2023
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