TY - JOUR
T1 - Global gradient estimates for nonlinear elliptic equations
AU - Ryu, Seungjin
N1 - Publisher Copyright:
© 2014 Korean Mathematical Society.
PY - 2014
Y1 - 2014
N2 - We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calderón-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.
AB - We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calderón-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.
KW - BMO space
KW - Calderón-Zygmund theory
KW - Global gradient estimate
KW - Nonlinear elliptic equation
KW - Reifenberg flat domain
UR - http://www.scopus.com/inward/record.url?scp=84908268764&partnerID=8YFLogxK
U2 - 10.4134/JKMS.2014.51.6.1209
DO - 10.4134/JKMS.2014.51.6.1209
M3 - Article
AN - SCOPUS:84908268764
SN - 0304-9914
VL - 51
SP - 1209
EP - 1220
JO - Journal of the Korean Mathematical Society
JF - Journal of the Korean Mathematical Society
IS - 6
ER -