Local W^{1,p}-regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts - Tuoc Phan (Electronic Journal of Differential Equations, 2017)
We study 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 $L^∞$-assumption on solutions by solutions in the John-Nirenberg BMO space. The results are also generalized to parabolic equations in divergence form with small oscillation elliptic symmetric coefficients and therefore improve many known results.