Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains

Abstract

We derive global gradient estimates in Morrey spaces for the weak solutions to discontinuous quasilinear elliptic equations related to important variational problems arising in models of linearly elastic laminates and composite materials. The principal coefficients of the quasilinear operator are supposed to be merely measurable in one variable and to have small-BMO seminorms in the remaining orthogonal directions, and the nonlinear terms are subject to controlled growth conditions with respect to the unknown function and its gradient. The boundary of the domain considered is Reifenberg flat which includes boundaries with rough fractal structure. As outgrowth of the main result we get global Holder continuity of the weak solution with exact value of the corresponding exponent.