Elliptic equations with measurable coefficients in Reifenberg domains

Sun-Sig Byun; Lihe Wang

doi:10.1016/j.aim.2010.05.014

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Elliptic equations with measurable coefficients in Reifenberg domains

Journal article

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Peer reviewed

Elliptic equations with measurable coefficients in Reifenberg domains

Sun-Sig Byun and Lihe Wang

Advances in mathematics (New York. 1965), Vol.225(5), pp.2648-2673

2010

DOI: 10.1016/j.aim.2010.05.014

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Abstract

We prove W 1 , p estimates for elliptic equations in divergence form under the assumption that for each point and for each sufficiently small scale there is a coordinate system so that the coefficients have small oscillation in ( n − 1 ) directions. We assume the boundary to be δ-Reifenberg flat and the coefficients having small oscillation in the flat direction of the boundary.

[formula omitted] space

Elliptic equation

Measurable coefficients

BMO space

Gradient estimate

Reifenberg domain

Details

Title: Subtitle: Elliptic equations with measurable coefficients in Reifenberg domains
Creators: Sun-Sig Byun - Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
Lihe Wang - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Resource Type: Journal article
Publication Details: Advances in mathematics (New York. 1965), Vol.225(5), pp.2648-2673
DOI: 10.1016/j.aim.2010.05.014
ISSN: 0001-8708
eISSN: 1090-2082
Publisher: Elsevier Inc
Language: English
Date published: 2010
Academic Unit: Mathematics
Record Identifier: 9984083856402771

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