The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg flat domains

• Autores: Sun-Sig Byun, Lihe Wang
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 1, 2005, págs. 245-272
• Idioma: inglés
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• Resumen

  • 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 $\delta$-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.