Elliptic equations with BMO coefficients in Reifenberg domains | Zendy

Byun SunSig | Zendy; Wang Lihe | Zendy

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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.

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