Tuoc Phan
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
-estimates for the gradients of weak solutions. Our results improve
the classical one to the borderline case by replacing the
-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.
Submitted December 31, 2016. Published March 20, 2017.
Math Subject Classifications: 35K10, 35K67, 35B45.
Key Words: Weighted Sobolev estimates; divergence-free drifts;
Muckenhoupt weights; Hardy-Littlewood maximal functions.
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Tuoc Phan Department of Mathematics University of Tennessee, Knoxville 227 Ayress Hall, 1403 Circle Drive Knoxville, TN 37996, USA email: phan@math.utk.edu |
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