Elliptic equations with measurable coefficients in Reifenberg domains |
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| Authors: | Sun-Sig Byun Lihe Wang |
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| Institution: | a Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
b Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA |
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| Abstract: | We prove W1,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. |
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| Keywords: | primary 35J15 secondary 35D10 |
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