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

Tuoc Phan

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arXiv · 1701.00417

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

Tuoc Phan

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Abstract

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 equations in divergence form with small oscillation elliptic symmetric coefficients and therefore improve many known results.

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Tuoc Phan. 2017-01-02. A note on local $W^{1,p}$-regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts. https://arxiv.org/abs/1701.00417

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