A Wpn-theory of parabolic equations with unbounded leading coefficients on non-smooth domains

Kyeong Hun Kim

doi:10.1016/j.jmaa.2008.09.058

A W_pⁿ-theory of parabolic equations with unbounded leading coefficients on non-smooth domains

Kyeong Hun Kim

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.

Original language	English
Pages (from-to)	294-305
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	350
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2008.09.058
Publication status	Published - 2009 Feb 1

Keywords

Hardy inequality
Non-smooth domains
Unbounded leading coefficients
Weighted Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2008.09.058

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title = "A Wpn-theory of parabolic equations with unbounded leading coefficients on non-smooth domains",

abstract = "We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and H{\"o}lder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.",

keywords = "Hardy inequality, Non-smooth domains, Unbounded leading coefficients, Weighted Sobolev spaces",

author = "Kim, {Kyeong Hun}",

note = "Funding Information: ✩ This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R01-2008-000-20010-0). E-mail address: kyeonghun@korea.ac.kr.",

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AU - Kim, Kyeong Hun

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Y1 - 2009/2/1

N2 - We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.

AB - We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any nonnegative real number, in particular, it can be fractional.

KW - Hardy inequality

KW - Non-smooth domains

KW - Unbounded leading coefficients

KW - Weighted Sobolev spaces

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