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arXiv · 2309.06295

A note on weak existence for singular SDEs

Lucio Galeati
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Abstract

Recently Krylov established weak existence of solutions to SDEs for integrable drifts in mixed Lebesgue spaces, whose exponents satisfy the condition $1/q+d/p\leq 1$, thus going below the celebrated Ladyzhenskaya-Prodi-Serrin condition. We present here a variant of such result, whose proof relies on an alternative technique, based on a partial Zvonkin transform; this allows for drifts with growth at infinity and/or in uniformly local Lebesgue spaces.

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Lucio Galeati. 2023-09-12. A note on weak existence for singular SDEs. https://arxiv.org/abs/2309.06295

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