Geodesic
On the Lower Bounded Slope Condition
Journal of convex analysis, Tome 14 (2007) no. 1, pp. 119-136 Cet article a éte moissonné depuis la source Heldermann Verlag

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Let $\Omega$ be a bounded open convex set in ${\mathbb R}^n$ and let $\phi \colon \Gamma:=\partial\Omega\to {\mathbb R}$ be a function defined on its boundary. The \textit{lower bounded slope condition} (on $\phi$) is a hypothesis recently introduced by F. Clarke [Ann. Scuola Norm. Sup. Pisa, in print], who has shown its relevance to regularity theory in the calculus of variations. It corresponds to a weaker version of the traditional \textit{bounded slope condition}, which also appears in the theory of elliptic differential equations. In this paper, we study the regularity properties of these functions and give intrinsic characterizations of them. Semiconvexity turns out to be a central tool in the proofs. 
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     author = {P. Bousquet},
     title = {On the {Lower} {Bounded} {Slope} {Condition}},
     journal = {Journal of convex analysis},
     pages = {119--136},
     year = {2007},
     volume = {14},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_1_JCA_2007_14_1_a9/}
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P. Bousquet. On the Lower Bounded Slope Condition. Journal of convex analysis, Tome 14 (2007) no. 1, pp. 119-136. http://geodesic.mathdoc.fr/item/JCA_2007_14_1_JCA_2007_14_1_a9/