The Calderón–Zygmund property for quasilinear divergence form equations over Reifenberg flat domains

The results by Palagachev (2009) [3] regarding global Hölder continuity for the weak solutions to quasilinear divergence form elliptic equations are generalized to the case of nonlinear terms with optimal growths with respect to the unknown function and its gradient. Moreover, the principal coefficients are discontinuous with discontinuity measured in terms of small BMOBMO norms and the underlying domain is supposed to have fractal boundary satisfying a condition of Reifenberg flatness. The results are extended to the case of parabolic operators as well.