Partial Hölder continuity for solutions of subquadratic elliptic systems in low dimensions

We consider weak solutions of second order nonlinear elliptic systems in divergence form under standard subquadratic growth conditions with boundary data of class C¹. In dimensions n∈{2,3} we prove that u is locally Hölder continuous for every exponent outside a singular set of Hausdorff dimension less than n−p. This result holds up to the boundary both for non-degenerate and degenerate systems. In the proof we apply the direct method and classical Morrey-type estimates introduced by Campanato.