Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains

Sun-Sig Byun; Lihe Wang

doi:10.1016/j.jde.2008.03.028

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Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains

Journal article

Open access

Peer reviewed

Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains

Sun-Sig Byun and Lihe Wang

Journal of Differential Equations, Vol.245(11), pp.3217-3252

2008

DOI: 10.1016/j.jde.2008.03.028

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Abstract

We study optimal W 2 , p -regularity for fourth-order parabolic equations with discontinuous coefficients in general domains. We obtain the global W 2 , p -regularity for each 1 < p < ∞ under the assumption that the coefficients have suitably small BMO semi-norm of weak type and the boundary of the domain is δ-Reifenberg flat. The situation of our main theorem arises when the conductivity on fractals is controlled by a random variable in the time direction.

Reifenberg domains

Fractals

[formula omitted] estimates

BMO space

Vitali covering lemma

Fourth-order parabolic equations

Details

Title: Subtitle: Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains
Creators: Sun-Sig Byun - Department of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
Lihe Wang - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Resource Type: Journal article
Publication Details: Journal of Differential Equations, Vol.245(11), pp.3217-3252
DOI: 10.1016/j.jde.2008.03.028
ISSN: 0022-0396
eISSN: 1090-2732
Publisher: Elsevier Inc
Language: English
Date published: 2008
Academic Unit: Mathematics
Record Identifier: 9984083261702771

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