We consider a relaxed notion of energy of non-parametric codimension one surfaces that takes into account area, mean curvature, and Gauss curvature. It is given by the best value obtained by approximation with inscribed polyhedral surfaces. The BV and measure properties of functions with finite relaxed energy are studied. Concerning the total mean and Gauss curvature, the classical counterexample by Schwarz-Peano to the definition of area is also analyzed.

中文翻译：

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表面的有界变化和松弛曲率

我们考虑了一个非参数余维一曲面的能量松弛概念，其中考虑了面积，平均曲率和高斯曲率。它是通过与内接多面体表面近似获得的最佳值给出的。研究了具有有限松弛能量的函数的BV和度量性质。关于总均值和高斯曲率，还分析了Schwarz-Peano对面积定义的经典反例。