# A note on local $W^{1,p}$-regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts

@article{Phan2017ANO, title={A note on local \$W^\{1,p\}\$-regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts}, author={Tuoc Van Phan}, journal={arXiv: Analysis of PDEs}, year={2017} }

We investigate weighted Sobolev regularity of weak solutions of non-homogeneous parabolic equations with singular divergence-free drifts. Assuming that the drifts satisfy some mild regularity conditions, we establish local weighted $L^p$-estimates for the gradients of weak solutions. Our results improve the classical one to the borderline case by replacing the $L^\infty$-assumption on solutions by solutions in the John-Nirenberg \textup{BMO} space. The results are also generalized to parabolic…

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