TY - JOUR
T1 - Weighted L p , q -estimates for higher order elliptic and parabolic systems with BMO x coefficients on Reifenberg flat domains
AU - Choi, Jongkeun
AU - Kim, Doyoon
N1 - Funding Information:
D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865).
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - We prove weighted L p , q -estimates for divergence type higher order elliptic and parabolic systems with irregular coefficients on Reifenberg flat domains. In particular, in the parabolic case the coefficients do not have any regularity assumptions in the time variable. As functions of the spatial variables, the leading coefficients are permitted to have small mean oscillations. The weights are in the class of Muckenhoupt weights A p . We also prove the solvability of the systems in weighted Sobolev spaces.
AB - We prove weighted L p , q -estimates for divergence type higher order elliptic and parabolic systems with irregular coefficients on Reifenberg flat domains. In particular, in the parabolic case the coefficients do not have any regularity assumptions in the time variable. As functions of the spatial variables, the leading coefficients are permitted to have small mean oscillations. The weights are in the class of Muckenhoupt weights A p . We also prove the solvability of the systems in weighted Sobolev spaces.
UR - http://www.scopus.com/inward/record.url?scp=85065477932&partnerID=8YFLogxK
U2 - 10.1007/s00526-019-1537-9
DO - 10.1007/s00526-019-1537-9
M3 - Article
AN - SCOPUS:85065477932
SN - 0944-2669
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 3
M1 - 90
ER -