TY - JOUR
T1 - Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains
AU - Byun, Sun Sig
AU - Ryu, Seungjin
AU - Wang, Lihe
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77954862931&partnerID=8YFLogxK
U2 - 10.1007/s00229-010-0373-1
DO - 10.1007/s00229-010-0373-1
M3 - Article
AN - SCOPUS:77954862931
SN - 0025-2611
VL - 133
SP - 225
EP - 245
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 1
ER -