Weighted W 1, p (·)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains

Let w be a Muckenhoupt A 2(ℝ n ) weight and Ω a bounded Reifenberg flat domain in ℝ n . Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition. In this article, the authors investigate the weighted W 1, p (·)(Ω, w)-regularity of the weak solutions of second order degenerate elliptic equations in divergence form with Dirichlet boundary condition, under the assumption that the degenerate coefficients belong to weighted BMO spaces with small norms.

Pointwise estimates for Stokes systems with BMO coefficients in Reifenberg domains

Pointwise estimates of weak solution pairs to a stationary Stokes system with small [Formula: see text] semi-norm coefficients are established in Reifenberg flat domains by using the restricted sharp maximal function. These pointwise estimates provide a unified treatment of the Calderón–Zygmund estimates for the solution pair to Stokes systems in [Formula: see text] and [Formula: see text] spaces.

Global W1,p(·) estimate for renormalized solutions of quasilinear equations with measure data on Reifenberg domains

In this paper, we prove the gradient estimate for renormalized solutions to quasilinear elliptic equations with measure data on variable exponent Lebesgue spaces with BMO coefficients in a Reifenberg flat domain.

Homogenization of the conormal derivative problem for elliptic systems in Reifenberg domains

We study homogenization of the conormal derivative problem for an elliptic system with discontinuous coefficients in a bounded domain. A uniform global [Formula: see text] estimate for [Formula: see text] is obtained under optimal assumptions that the coefficients have a small bounded mean oscillation (BMO) seminorm and the domain is a [Formula: see text]-Reifenberg flat domain whose boundary might be fractal.