TY - JOUR
T1 - Elliptic obstacle problems with measurable nonlinearities in non-smooth domains
AU - Kim, Youchan
AU - Ryu, Seungjin
N1 - Publisher Copyright:
© 2019 Korean Mathematical Society.
PY - 2019
Y1 - 2019
N2 - The Calderón-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity a(ξ; x 1 ; xʹ) is assumed to be only measurable in one spatial variable x 1 and has locally small BMO seminorm in the other spatial variables xʹ, uniformly in ξ variable. Regarding non-smooth domains, we assume that the boundaries are locally at in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.
AB - The Calderón-Zygmund type estimate is proved for elliptic obstacle problems in bounded non-smooth domains. The problems are related to divergence form nonlinear elliptic equation with measurable nonlinearities. Precisely, nonlinearity a(ξ; x 1 ; xʹ) is assumed to be only measurable in one spatial variable x 1 and has locally small BMO seminorm in the other spatial variables xʹ, uniformly in ξ variable. Regarding non-smooth domains, we assume that the boundaries are locally at in the sense of Reifenberg. We also investigate global regularity in the settings of weighted Orlicz spaces for the weak solutions to the problems considered here.
KW - BMO
KW - Calderón-Zygmund type estimate
KW - Measurable nonlinearity
KW - Nonlinear elliptic obstacle problem
KW - Reifenberg at domain
UR - http://www.scopus.com/inward/record.url?scp=85062683099&partnerID=8YFLogxK
U2 - 10.4134/JKMS.j180157
DO - 10.4134/JKMS.j180157
M3 - Article
AN - SCOPUS:85062683099
SN - 0304-9914
VL - 56
SP - 239
EP - 263
JO - Journal of the Korean Mathematical Society
JF - Journal of the Korean Mathematical Society
IS - 1
ER -