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

Kim, Kyeong-Hun; Lee, Kijung

doi:10.1016/j.jde.2012.08.002

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

Kim, Kyeong-Hun;
Lee, Kijung

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초록

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. (C) 2012 Elsevier Inc. All rights reserved.

키워드

Parabolic equations; Weighted Sobolev spaces; L-p-theory; BMO coefficients; VMO coefficients; SOBOLEV SPACE THEORY; ELLIPTIC-EQUATIONS; DIFFERENTIAL-EQUATIONS; DIRICHLET PROBLEM; VMO

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

저자: Kim, Kyeong-Hun; Lee, Kijung

DOI: 10.1016/j.jde.2012.08.002

발행일: 2013-01-15

유형: Article

저널명: Journal of Differential Equations

권: 254

호: 2

페이지: 368 ~ 407