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On divergence-free drifts

Abstract:

We investigate the validity and failure of Liouville theorems and Harnack inequalities for parabolic and elliptic operators with low regularity coefficients. We are particularly interested in operators of the form ∂t-Δ+b-∇ resp. -Δ+b-∇ with a divergence-free drift b. We prove the Liouville theorem and Harnack inequality when b∈L∞(BMO-1) resp. b∈BMO-1 and provide a counterexample demonstrating sharpness of our conditions on the drift. Our results generalize to divergence-form operators with an...

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Publication status:
Published

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Publisher copy:
10.1016/j.jde.2011.08.039

Authors


Seregin, G More by this author
Silvestre, L More by this author
Journal:
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume:
252
Issue:
1
Pages:
505-540
Publication date:
2012
DOI:
EISSN:
1090-2732
ISSN:
0022-0396
URN:
uuid:b3108ee2-36e4-4167-b16f-3aa3a09bd1a8
Source identifiers:
196153
Local pid:
pubs:196153
Language:
English

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