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Elliptic equations with BMO coefficients in Lipschitz domains


Author: Sun-Sig Byun
Journal: Trans. Amer. Math. Soc. 357 (2005), 1025-1046
MSC (2000): Primary 35R05, 35R35; Secondary 35J15, 35J25
DOI: https://doi.org/10.1090/S0002-9947-04-03624-4
Published electronically: May 28, 2004
MathSciNet review: 2110431
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Abstract: In this paper, we study inhomogeneous Dirichlet problems for elliptic equations in divergence form. Optimal regularity requirements on the coefficients and domains for the $W^{1,p} (1<p<\infty)$ estimates are obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO semi-norms. The domain is supposed to have Lipschitz boundary with small Lipschitz constant. These conditions for the $W^{1,p}$ theory do not just weaken the requirements on the coefficients; they also lead to a more general geometric condition on the domain.


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Additional Information

Sun-Sig Byun
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Address at time of publication: Department of Mathematics, University of California, Irvine, California 92697
Email: byun@math.uci.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03624-4
Keywords: Elliptic equations, Lipschitz domains, BMO, maximal function, Vitali covering lemma, compactness method
Received by editor(s): July 23, 2003
Published electronically: May 28, 2004
Additional Notes: This work was supported in part by NSF Grant #0100679
Article copyright: © Copyright 2004 American Mathematical Society

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