Abstract
Given a semi-convex functionu: ω⊂R n→R and an integerk≡[0,1,n], we show that the set ∑k defined by
is countably ℋn-k i.e., it is contained (up to a ℋn-k-negligible set) in a countable union ofC 1 hypersurfaces of dimensions (n−k).
Moreover, we show that
for any open set ω′⊂⊂ω.
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Work (partially) supported by the Research Project, ”Equazioni di evoluzione ed applicazioni fisico-matematiche“ (M.U.R.S.T.-Italy)
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Alberti, G., Ambrosio, L. & Cannarsa, P. On the singularities of convex functions. Manuscripta Math 76, 421–435 (1992). https://doi.org/10.1007/BF02567770
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DOI: https://doi.org/10.1007/BF02567770