On the generalized mean curvature |
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Authors: | Elisabetta Barozzi Eduardo Gonzalez Umberto Massari |
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Institution: | 1. Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38100, Povo (TN), Italy 2. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Padova, Via Trieste 63, 35121, Padova, Italy 3. Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100, Ferrara, Italy
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Abstract: | We study some properties of graphs whose mean curvature (in distributional sense) is a vector Radon measure. In particular, we prove that the distributional mean curvature of the graph of a Lipschitz continuous function u is a measure if and only if the distributional divergence of T u is a measure. This equivalence fails to be true if Lipschitz continuity is relaxed, as it is shown in a couple of examples. Finally, we prove a theorem of approximation in W (1,1) and in the sense of mean curvature of C 2 graphs by polyhedral graphs. A number of examples illustrating different situations which can occur complete the work. |
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