A weighted L p-theory for parabolic PDEs with BMO coefficients on C 1-domains

Kyeong Hun Kim; Kijung Lee

doi:10.1016/j.jde.2012.08.002

A weighted L _p-theory for parabolic PDEs with BMO coefficients on C ¹-domains

Kyeong Hun Kim, Kijung Lee

Department of Mathematics

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

6 Citations (Scopus)

Abstract

In this paper we present a weighted L _p-theory of second-order parabolic partial differential equations defined on C ¹ domains. The leading coefficients are assumed to be measurable in time variable and have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation) with respect to space variables, and lower order coefficients are allowed to be unbounded and to blow up near the boundary. Our BMO condition is slightly relaxed than the others in the literature.

Original language	English
Pages (from-to)	368-407
Number of pages	40
Journal	Journal of Differential Equations
Volume	254
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2012.08.002
Publication status	Published - 2013 Jan 15

Keywords

BMO coefficients
L -theory
Parabolic equations
VMO coefficients
Weighted Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2012.08.002

Cite this

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title = "A weighted L p-theory for parabolic PDEs with BMO coefficients on C 1-domains",

abstract = "In this paper we present a weighted L p-theory of second-order parabolic partial differential equations defined on C 1 domains. The leading coefficients are assumed to be measurable in time variable and have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation) with respect to space variables, and lower order coefficients are allowed to be unbounded and to blow up near the boundary. Our BMO condition is slightly relaxed than the others in the literature.",

keywords = "BMO coefficients, L -theory, Parabolic equations, VMO coefficients, Weighted Sobolev spaces",

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

note = "Funding Information: E-mail addresses: kyeonghun@korea.ac.kr (K.-H. Kim), kijung@ajou.ac.kr (K. Lee). 1 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0015961). 2 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0005597).",

year = "2013",

month = jan,

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doi = "10.1016/j.jde.2012.08.002",

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journal = "Journal of Differential Equations",

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AU - Lee, Kijung

N1 - Funding Information: E-mail addresses: kyeonghun@korea.ac.kr (K.-H. Kim), kijung@ajou.ac.kr (K. Lee). 1 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0015961). 2 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0005597).

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N2 - In this paper we present a weighted L p-theory of second-order parabolic partial differential equations defined on C 1 domains. The leading coefficients are assumed to be measurable in time variable and have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation) with respect to space variables, and lower order coefficients are allowed to be unbounded and to blow up near the boundary. Our BMO condition is slightly relaxed than the others in the literature.

AB - In this paper we present a weighted L p-theory of second-order parabolic partial differential equations defined on C 1 domains. The leading coefficients are assumed to be measurable in time variable and have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation) with respect to space variables, and lower order coefficients are allowed to be unbounded and to blow up near the boundary. Our BMO condition is slightly relaxed than the others in the literature.

KW - BMO coefficients

KW - L -theory

KW - Parabolic equations

KW - VMO coefficients

KW - Weighted Sobolev spaces

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