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arXiv · 2110.11232

Sharp solvability for singular SDEs

Damir Kinzebulatov·Yuliy A. Semenov
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Abstract

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 $L^p$ variant of De Giorgi's method.

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Damir Kinzebulatov, Yuliy A. Semenov. 2021-10-21. Sharp solvability for singular SDEs. https://arxiv.org/abs/2110.11232

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