Lp-estimates for time fractional parabolic equations with coefficients measurable in time

Hongjie Dong; Doyoon Kim

doi:10.1016/j.aim.2019.01.016

L_p-estimates for time fractional parabolic equations with coefficients measurable in time

Hongjie Dong, Doyoon Kim

Department of Mathematics

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

30 Citations (Scopus)

Abstract

We establish the L_p-solvability for time fractional parabolic equations when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend a recent result in [6] to a large extent.

Original language	English
Pages (from-to)	289-345
Number of pages	57
Journal	Advances in Mathematics
Volume	345
DOIs	https://doi.org/10.1016/j.aim.2019.01.016
Publication status	Published - 2019 Mar 17

Keywords

Measurable coefficients
Parabolic equation
Small mean oscillations
Time fractional derivative

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1016/j.aim.2019.01.016

Cite this

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title = "Lp-estimates for time fractional parabolic equations with coefficients measurable in time",

abstract = "We establish the Lp-solvability for time fractional parabolic equations when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend a recent result in [6] to a large extent.",

keywords = "Measurable coefficients, Parabolic equation, Small mean oscillations, Time fractional derivative",

author = "Hongjie Dong and Doyoon Kim",

note = "Funding Information: H. Dong was partially supported by the NSF under agreement DMS-1600593.D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03934369). Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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AB - We establish the Lp-solvability for time fractional parabolic equations when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend a recent result in [6] to a large extent.

KW - Measurable coefficients

KW - Parabolic equation

KW - Small mean oscillations

KW - Time fractional derivative

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