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arXiv · 2604.11960

On the heat equation with singular drift

N. V. Krylov
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Abstract

We prove the maximum modulus estimates in terms of the $L_{q,p}$-norm of the free term for solutions of the heat equation with Morrey drift for any $q,p$ satisfying $d/p+2/q<2$ and any order of integration in the definition of the $L_{q,p}$-norm. An application to the case of $b$ satisfying the Ladyzhenskaya-Prodi-Serrin condition is given. The technique is easily adaptable to equations with Laplacians of order $\geq 1$.

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N. V. Krylov. 2026-04-13. On the heat equation with singular drift. https://arxiv.org/abs/2604.11960

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