The mean curvature of a Lipschitz continuous manifold

Barozzi, Elisabetta, Gonzalez, Eduardo, and Massari, Umberto. "The mean curvature of a Lipschitz continuous manifold." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.4 (2003): 257-277. <http://eudml.org/doc/252366>.

@article{Barozzi2003,
abstract = {The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of $\partial E$ by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of $\partial E$ is the weak limit (in the sense of distributions) of the mean curvatures of a sequence of regular $n$-dimensional manifolds $M_\{j\}$ convergent to $\partial E$. The manifolds $M_\{j\}$ are closely related to the level surfaces of the variational mean curvature $H_\{E\}$ of $E$.},
author = {Barozzi, Elisabetta, Gonzalez, Eduardo, Massari, Umberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Calculus of Variations; Geometric Measure Theory; Functions of Bounded Variation; Mean Curvature; functions of bounded variation; mean variational mean curvature},
language = {eng},
month = {12},
number = {4},
pages = {257-277},
publisher = {Accademia Nazionale dei Lincei},
title = {The mean curvature of a Lipschitz continuous manifold},
url = {http://eudml.org/doc/252366},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Barozzi, Elisabetta
AU - Gonzalez, Eduardo
AU - Massari, Umberto
TI - The mean curvature of a Lipschitz continuous manifold
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/12//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 4
SP - 257
EP - 277
AB - The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of $\partial E$ by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of $\partial E$ is the weak limit (in the sense of distributions) of the mean curvatures of a sequence of regular $n$-dimensional manifolds $M_{j}$ convergent to $\partial E$. The manifolds $M_{j}$ are closely related to the level surfaces of the variational mean curvature $H_{E}$ of $E$.
LA - eng
KW - Calculus of Variations; Geometric Measure Theory; Functions of Bounded Variation; Mean Curvature; functions of bounded variation; mean variational mean curvature
UR - http://eudml.org/doc/252366
ER -