Local W^{1,p}-regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts
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Date
2017-03-20
Authors
Phan, Tuoc
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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 Lp-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.
Description
Keywords
Weighted Sobolev estimates, Divergence-free drifts, Muckenhoupt weights, Hardy-Littlewood maximal functions
Citation
Phan, T. (2017). Local W^{1,p}-regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts. <i>Electronic Journal of Differential Equations, 2017</i>(75), pp. 1-22.
Rights
Attribution 4.0 International