Calculus of Variations and Geometric Measure Theory

E. Paolini

Regularity for minimal boundaries in $R^n$ with mean curvature in $L^n$

created on 11 Sep 1998
modified by paolini on 16 Mar 2022


Published Paper

Inserted: 11 sep 1998
Last Updated: 16 mar 2022

Journal: manuscripta math.
Volume: 97
Pages: 15-35
Year: 1998
Doi: 10.1007/s002290050082


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