PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS IN WEIGHTED SOBOLEV SPACES

Doyoon Kim; Kyeong Hun Kim; Kijung Lee

doi:10.3934/cpaa.2022062

PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS IN WEIGHTED SOBOLEV SPACES

Doyoon Kim, Kyeong Hun Kim, Kijung Lee

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We present a weighted L_p-theory of parabolic systems on a half space R^d₊. The leading coefficients are assumed to be only measurable in time t and have small bounded mean oscillations (BMO) with respect to the spatial variables x, and the lower order coefficients are allowed to blow up near the boundary.

Original language	English
Pages (from-to)	2587-2613
Number of pages	27
Journal	Communications on Pure and Applied Analysis
Volume	21
Issue number	8
DOIs	https://doi.org/10.3934/cpaa.2022062
Publication status	Published - 2022 Aug

Bibliographical note

Funding Information:
2020 Mathematics Subject Classification. 35K51, 35R05. Key words and phrases. sharp/maximal functions, parabolic systems, weighted Sobolev spaces, measurable coefficients. The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1084683).The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01003354). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058988). ∗Corresponding author.

Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

Keywords

measurable coefficients
parabolic systems
sharp/maximal functions
weighted Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.3934/cpaa.2022062

Cite this

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title = "PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS IN WEIGHTED SOBOLEV SPACES",

abstract = "We present a weighted Lp-theory of parabolic systems on a half space Rd+. The leading coefficients are assumed to be only measurable in time t and have small bounded mean oscillations (BMO) with respect to the spatial variables x, and the lower order coefficients are allowed to blow up near the boundary.",

keywords = "measurable coefficients, parabolic systems, sharp/maximal functions, weighted Sobolev spaces",

author = "Doyoon Kim and Kim, {Kyeong Hun} and Kijung Lee",

note = "Funding Information: 2020 Mathematics Subject Classification. 35K51, 35R05. Key words and phrases. sharp/maximal functions, parabolic systems, weighted Sobolev spaces, measurable coefficients. The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1084683).The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01003354). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058988). ∗Corresponding author. Publisher Copyright: {\textcopyright} 2022 American Institute of Mathematical Sciences. All rights reserved.",

year = "2022",

month = aug,

doi = "10.3934/cpaa.2022062",

language = "English",

volume = "21",

pages = "2587--2613",

journal = "Communications on Pure and Applied Analysis",

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AU - Kim, Doyoon

AU - Kim, Kyeong Hun

AU - Lee, Kijung

N1 - Funding Information: 2020 Mathematics Subject Classification. 35K51, 35R05. Key words and phrases. sharp/maximal functions, parabolic systems, weighted Sobolev spaces, measurable coefficients. The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1084683).The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01003354). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058988). ∗Corresponding author. Publisher Copyright: © 2022 American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/8

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N2 - We present a weighted Lp-theory of parabolic systems on a half space Rd+. The leading coefficients are assumed to be only measurable in time t and have small bounded mean oscillations (BMO) with respect to the spatial variables x, and the lower order coefficients are allowed to blow up near the boundary.

AB - We present a weighted Lp-theory of parabolic systems on a half space Rd+. The leading coefficients are assumed to be only measurable in time t and have small bounded mean oscillations (BMO) with respect to the spatial variables x, and the lower order coefficients are allowed to blow up near the boundary.

KW - measurable coefficients

KW - parabolic systems

KW - sharp/maximal functions

KW - weighted Sobolev spaces

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DO - 10.3934/cpaa.2022062

M3 - Article

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VL - 21

SP - 2587

EP - 2613

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 8

ER -

PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS IN WEIGHTED SOBOLEV SPACES

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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