Elliptic equations with BMO coefficients in Lipschitz domains
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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.References
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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
- MR Author ID: 738383
- Email: byun@math.uci.edu
- Received by editor(s): July 23, 2003
- Published electronically: May 28, 2004
- Additional Notes: This work was supported in part by NSF Grant #0100679
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2110431