An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives

Hongjie Dong; Doyoon Kim

doi:10.1016/j.aim.2020.107494

An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives

Research output: Contribution to journal › Article › peer-review

Abstract

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 L_p-estimates without weights.

Original language	English
Article number	107494
Journal	Advances in Mathematics
Volume	377
DOIs	https://doi.org/10.1016/j.aim.2020.107494
Publication status	Published - 2021 Jan 22

Keywords

Mean oscillation estimates
Measurable coefficients
Parabolic equation
Time fractional derivative

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.aim.2020.107494

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title = "An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives",

abstract = "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.",

keywords = "Mean oscillation estimates, Measurable coefficients, Parabolic equation, Time fractional derivative",

author = "Hongjie Dong and Doyoon Kim",

note = "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). Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

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AU - Kim, Doyoon

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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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DO - 10.1016/j.aim.2020.107494

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JO - Advances in Mathematics

JF - Advances in Mathematics

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An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives

Abstract

Keywords

ASJC Scopus subject areas

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