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The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg flat domains

Published online by Cambridge University Press:  16 December 2004

Sun-Sig Byun  and
Lihe Wang
Sun-Sig Byun
Affiliation:
Department of Mathematics, University of California, Irvine, CA 92697, USA. E-mail: byun@math.uci.edu
Lihe Wang
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA and Department of Mathematics, Xian Jiaotong University, Xian 710049, China. E-mail: lwang@math.uiowa.edu
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Abstract

We study the inhomogeneous conormal derivative problem for the divergence form elliptic equation, assuming that the principal coefficients belong to the BMO space with small BMO semi-norms and that the boundary is $\delta$-Reifenberg flat. These conditions for the $W^{1, p}$-theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domain. In fact, the Reifenberg flatness is the minimal regularity condition for the $W^{1, p}$-theory.

Keywords

Reifenberg flatnessthe maximal functionVitali covering lemma35R05 (primary)35J15 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 1 , January 2005 , pp. 245 - 272
Copyright
2004 London Mathematical Society

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Footnotes

This work was supported in part by NSF Grant #0100679.