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The mean curvature of a Lipschitz continuous manifold

Elisabetta Barozzi;  Eduardo Gonzalez;  Umberto Massari — 2003

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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 ∂ ⁡ 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 ∂ ⁡ E is the weak limit (in the sense of distributions) of the mean...

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