The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg flat domains
Sun‐Sig Byun, Lihe Wang · Proceedings of the London Mathematical Society · 2004
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 W1, 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 W1, p-theory. 2000 Mathematics Subject Classification 35R05 (primary), 35J15 (secondary).