Journal article
Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains
Manuscripta mathematica, Vol.133(1), pp.225-245
09/2010
DOI: 10.1007/s00229-010-0373-1
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.
Details
- Title: Subtitle
- Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains
- Creators
- Sun-Sig Byun - Department of Mathematics and Research Institute of Mathematics Seoul National University Seoul 151-747 KoreaSeungjin Ryu - Department of Mathematics and Research Institute of Mathematics Seoul National University Seoul 151-747 KoreaLihe Wang - Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 P.R. China
- Resource Type
- Journal article
- Publication Details
- Manuscripta mathematica, Vol.133(1), pp.225-245
- Publisher
- Springer-Verlag
- DOI
- 10.1007/s00229-010-0373-1
- ISSN
- 0025-2611
- eISSN
- 1432-1785
- Language
- English
- Date published
- 09/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9984083895302771
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