*Published Paper*

**Inserted:** 11 nov 2009

**Last Updated:** 10 jan 2013

**Journal:** J. Math. Anal. Appl.

**Volume:** 354

**Number:** 1

**Pages:** 301-318

**Year:** 2009

**Doi:** 10.1016/j.jmaa.2008.12.042

**Abstract:**

We consider weak solutions of second order nonlinear elliptic systems in divergence form under standard subquadratic growth conditions with boundary data of class $C^1$. In dimensions $n \in \{2,3\}$ we prove that $u$ is locally Hölder continuous for every exponent $\lambda \in (0,1-\frac{n-2}{p})$ 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.

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