Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains

Sun Sig Byun, Seungjin Ryu, Lihe Wang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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 W1,p, 1 < p < ∞, regularity. It is proved that such a W1,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.

Original languageEnglish
Pages (from-to)225-245
Number of pages21
JournalManuscripta Mathematica
Volume133
Issue number1
DOIs
StatePublished - 2010

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