Non-linear elliptic systems with measure-valued right hand side

Abstract: "We prove existence of a solution u for the nonlinear elliptic system -div [sigma](x,u,Du) = [mu] in D(́[omega]), u = O on [delta omega] where [mu] is Radon measure on [omega] with finite mass. In particular we show that if the coercivity rate of [delta] lies in the range (1,2 - 1/n] then u is approximately differentiable and the equation holds with Du replaced by ap Du. The proof relies on an approximation of [mu] by smooth functions f[subscript k] and a compactness result for the corresponding solutions u[subscript k]. This follows from a detailed analysis of the Young measure [[delta subscript u(x)][circled x] v[subscript x]] generated by the sequence [(u[subscript k], Du[subscript k])] and the div-curl type inequality [< or =] [⁻sigma](x) for the weak limit [⁻sigma] of the sequence [[sigma](·,u[subscript k], Du[subscript k])]."