C0,α partial regularity result for elliptic systems with discontinuous coefficients and Orlicz growth

This paper is devoted to the study of C0,α-regularity for weak solutions to elliptic systems in divergence form. The model of our interest is −div(μ(x)A(x,Du))=B(x,Du), where the coefficient μ is discontinuous and x∈Ω, with Ω a bounded open subset of Rn. In particular, we assume the matrix A satisfies a G growth condition in Orlicz spaces, and the inhomogeneity B satisfies a controllable, or a critical, growth.