*Published Paper*

**Inserted:** 11 sep 1998

**Last Updated:** 28 nov 2016

**Journal:** manuscripta math.

**Volume:** 97

**Pages:** 15-35

**Year:** 1998

**Doi:** 10.1007/s002290050082

**Abstract:**

Let $E_0\subset R^n$ be a minimal set with mean curvature in $L^n$ that is a minimum of the functional $E\mapsto P(E,\Omega)+\int_{E\cap\Omega} H$, where $\Omega\subset R^n$ is open and $H\in L^n(\Omega)$. We prove that if $2\le n\le 7$ then $\partial E_0$ can be parametrized over the $(n-1)$-dimensional disk with a $C^{0,\alpha}$ mapping with $C^{0,\alpha}$ inverse.

**Keywords:**
regularity, minimal surfaces

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