TY - JOUR
T1 - An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives
AU - Dong, Hongjie
AU - Kim, Doyoon
N1 - Funding Information:
H. Dong is partially supported by the Simons Foundation, grant # 709545.D. Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1084683).
PY - 2020
Y1 - 2020
N2 - We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [5] for unmixed Lp-estimates without weights.
AB - We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [5] for unmixed Lp-estimates without weights.
KW - Mean oscillation estimates
KW - Measurable coefficients
KW - Parabolic equation
KW - Time fractional derivative
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U2 - 10.1016/j.aim.2020.107494
DO - 10.1016/j.aim.2020.107494
M3 - Article
AN - SCOPUS:85096170429
VL - 377
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
M1 - 107494
ER -