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 C2 graphs by polyhedral graphs. A number of examples illustrating different situations which can occur complete the work.
On the generalized mean curvature
MASSARI, Umberto
2010
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 C2 graphs by polyhedral graphs. A number of examples illustrating different situations which can occur complete the work.File in questo prodotto:
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