TY - JOUR
T1 - Global gradient estimates for parabolic equations with measurable nonlinearities
AU - Kim, Youchan
AU - Ryu, Seungjin
N1 - Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2017/11
Y1 - 2017/11
N2 - We establish a global Calderón–Zygmund theory of nonlinear parabolic equations with measurable nonlinearities in divergence form by proving that the spatial gradient of a weak solution is as integrable as the inhomogeneous term. Nonlinearity a(ξ,x,t) is assumed to be only measurable in one spatial variable and has locally small BMO semi-norm in the other spatial and time variables, uniformly with respect to ξ variable. The boundary of the bounded domain can be beyond the Lipschitz category, but it is well trapped in two narrow strips at each point and at each scale.
AB - We establish a global Calderón–Zygmund theory of nonlinear parabolic equations with measurable nonlinearities in divergence form by proving that the spatial gradient of a weak solution is as integrable as the inhomogeneous term. Nonlinearity a(ξ,x,t) is assumed to be only measurable in one spatial variable and has locally small BMO semi-norm in the other spatial and time variables, uniformly with respect to ξ variable. The boundary of the bounded domain can be beyond the Lipschitz category, but it is well trapped in two narrow strips at each point and at each scale.
KW - Calderón–Zygmund type estimate
KW - Measurable nonlinearity
KW - Nonlinear parabolic equation
KW - Reifenberg flat domain
UR - http://www.scopus.com/inward/record.url?scp=85029544410&partnerID=8YFLogxK
U2 - 10.1016/j.na.2017.08.009
DO - 10.1016/j.na.2017.08.009
M3 - Article
AN - SCOPUS:85029544410
SN - 0362-546X
VL - 164
SP - 77
EP - 99
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -