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Elliptic equations with BMO coefficients in Reifenberg domains
Author(s) -
Byun SunSig,
Wang Lihe
Publication year - 2004
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20037
Subject(s) - mathematics , divergence (linguistics) , domain (mathematical analysis) , mathematical analysis , dirichlet distribution , space (punctuation) , principal part , pure mathematics , principal (computer security) , boundary value problem , philosophy , linguistics , computer science , operating system
The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are studied. Optimal regularity requirements on the coefficients and domains for the W 1, p theory, 1 < p < ∞, are obtained. The principal coefficients are supposed to be in the John‐Nirenberg space with small BMO seminorms. The domain is a Reifenberg domain. These conditions for the W 1, p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains. In fact, these domains might have fractal dimensions. © 2004 Wiley Periodicals, Inc.