Local W^{1,p}-regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts
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 imp...
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| Format: | Article |
| Language: | English |
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Texas State University
2017-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/75/abstr.html |
| Summary: | 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 $L^\infty$-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. |
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| ISSN: | 1072-6691 |