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In this paper, we are concerned with the nonlinear elliptic systems in divergence form under controllable growth condition. We prove that the weak solution u is locally Hölder continuous besides a singular set by using the direct method and classical Morrey-type estimates. Here the Hausdorff dimension of the singular set is less than n - p {n-p}. This result not only holds in the interior, but also holds up to the boundary. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with subquadratic homogeneity elliptic problems with VMO-coefficients in divergence form. We obtain that the weak solution u is locally Hölder continuous besides a singular set by using A -harmonic approximation, where the Hölder exponent α ∈ ( 0 , 1 ) . The Hausdorff dimension of the singular set is less than n − p . [ABSTRACT FROM AUTHOR]