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

Hongjie Dong; Doyoon Kim

doi:10.1016/j.jfa.2019.108338

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

Hongjie Dong, Doyoon Kim

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

13 Citations (Scopus)

Abstract

In this paper, we establish L_p-estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean oscillations with respect to the other variables. The corresponding results for equations on a half space are also derived.

Original language	English
Article number	108338
Journal	Journal of Functional Analysis
Volume	278
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2019.108338
Publication status	Published - 2020 Feb 1

Keywords

Measurable coefficients
Parabolic equations
Small mean oscillations
Time fractional derivative

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2019.108338

Cite this

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

abstract = "In this paper, we establish Lp-estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean oscillations with respect to the other variables. The corresponding results for equations on a half space are also derived.",

keywords = "Measurable coefficients, Parabolic equations, 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 - In this paper, we establish Lp-estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean oscillations with respect to the other variables. The corresponding results for equations on a half space are also derived.

KW - Measurable coefficients

KW - Parabolic equations

KW - Small mean oscillations

KW - Time fractional derivative

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