Calculus of Variations and Geometric Measure Theory

D. Mucci - A. Saracco

Bounded variation and relaxed curvature of surfaces

created by mucci on 25 Jul 2018
modified on 17 May 2020


Published Paper

Inserted: 25 jul 2018
Last Updated: 17 may 2020

Journal: Milan Journal of Mathematics
Year: 2020

Published online:28 March 2020


We consider a relaxed notion of energy of non-parametric codimension one surfaces that takes account of 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.

Keywords: curvature of surfaces; polyhedral surfaces; bounded variation