Weighted estimates for generalized steady Stokes systems in nonsmooth domains

摘要

We consider a generalized steady Stokes system with discontinuous coefficients in a nonsmooth domain when the inhomogeneous term belongs to a weighted L-q space for 2 < q < infinity. We prove the global weighted L-q-estimates for the gradient of the weak solution and an associated pressure under the assumptions that the coefficients have small bounded mean oscillation semi-norms and the domain is sufficiently flat in the Reifenberg sense. On the other hand, a given weight is assumed to belong to a Muckenhoupt class. Our result generalizes the global W-1.q estimate of Calderon-Zygmund with respect to the Lebesgue measure for the Stokes system in a Lipschitz domain. Published by AIP Publishing.