Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains |
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Authors: | Sun-Sig Byun Seungjin Ryu Lihe Wang |
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Affiliation: | 1. Department of Mathematics and Research Institute of Mathematics, Seoul National University, Seoul, 151-747, Korea 2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA 3. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China
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Abstract: | We consider an elliptic system in divergence form with measurable coefficients in a nonsmooth bounded domain to find a minimal regularity requirement on the coefficients and a lower level of geometric assumption on the boundary of the domain for a global W 1,p , 1 < p < ∞, regularity. It is proved that such a W 1,p regularity is still available under the assumption that the coefficients are merely measurable in one variable and have small BMO semi-norms in the other variables while the domain can be locally approximated by a hyperplane, a so called δ-Reifenberg domain, which is beyond the Lipschitz category. This regularity easily extends to a certain Orlicz-Sobolev space. |
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