Variable Lorentz estimate for stationary Stokes system with partially BMO coefficients (Q2062527)

The authors study regularity issues for the weak solution \((u,P)\) of the Dirichlet problem for the stationary Stokes system \[ \begin{cases} D_\alpha\big(\mathbf{A}^{\alpha\beta}(x)D_\beta u\big)+\nabla P=D_\alpha f_\alpha & \text{in}\ \Omega,\\ \text{div}\, u=g & \text{in}\ \Omega,\\ u=0 & \text{on}\ \partial\Omega, \end{cases} \] where \(\Omega\subset\mathbb{R}^n\) is a bounded domain with Reifenberg-flat boundary and the coeficient matrix is uniformly elliptic with entries which are partially small-BMO. The main result of the paper states Calderón--Zygmund type estimate in Lorentz spaces for the \(p(x)\)-power of \((\nabla u, P)\) with log-Hölder continuous \(p(x).\)