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The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg Flat Domains
Author(s) -
Byun SunSig,
Wang Lihe
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014960
Subject(s) - mathematics , flatness (cosmology) , divergence (linguistics) , mathematical analysis , domain (mathematical analysis) , mathematics subject classification , boundary (topology) , space (punctuation) , principal part , boundary value problem , pure mathematics , physics , philosophy , linguistics , cosmology , quantum mechanics
We study the inhomogeneous conormal derivative problem for the divergence form elliptic equation, assuming that the principal coefficients belong to the BMO space with small BMO semi‐norms and that the boundary is δ‐Reifenberg flat. 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 domain. In fact, the Reifenberg flatness is the minimal regularity condition for the W 1, p ‐theory. 2000 Mathematics Subject Classification 35R05 (primary), 35J15 (secondary).