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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Quasilinear elliptic equations with BMO coefficients in Lipschitz domains


Authors: Sun-Sig Byun and Lihe Wang
Journal: Trans. Amer. Math. Soc. 359 (2007), 5899-5913
MSC (2000): Primary 35R05, 35R35; Secondary 35J15, 35J25
DOI: https://doi.org/10.1090/S0002-9947-07-04238-9
Published electronically: June 26, 2007
MathSciNet review: 2336309
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Abstract: We obtain a global $ W^{1,q}$ estimate for the weak solution to an elliptic partial differential equation of $ p$-Laplacian type with BMO coefficients in a Lipschitz domain with small Lipschitz constant.


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Additional Information

Sun-Sig Byun
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: byun@math.snu.ac.kr

Lihe Wang
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 – and – College of Sciences, Xian Jiaotong University, Xian 710049, People’s Republic of China
Email: lwang@math.uiowa.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04238-9
Keywords: $W^{1,p}$ estimates, quasilinear elliptic equations, BMO space, Lipschitz domain, maximal function, Vitali covering lemma
Received by editor(s): August 5, 2005
Published electronically: June 26, 2007
Additional Notes: The first author was supported in part by KRF-2005-003-C00016.
The second author was supported in part by NSF Grant #0401261.
Article copyright: © Copyright 2007 American Mathematical Society