Lipschitz kernel of a closed set-valued map (Q1583986)

This paper concerns with Lipschitz selection of set-valued maps. The Lipschitz continuity of a set-valued map is characterized through a discriminating property introduced by \textit{P. Cardaliaguet} in the context of differential games [SIAM J. Control Optimization 34, No. 4, 1441-1460 (1996; Zbl 0853.90136)]. This allows to derive algorithms to determine the largest Lipschitz continuous (within advance fixed Lipschitz constant) set-valued map contained in [\textit{P. Cardaliaguet}, \textit{M. Quincampoix} and \textit{P. Saint-Pierre}, C. R. Acad. Sci., Paris, Sér. I 321, No. 12, 1543-1548 (1995; Zbl 0842.90138)]. The author also proposes an extension of sup-convolution of functions for set-valued maps and he discusses the link between this notion -- called Pasch-Hausdorff envelope in the present paper -- and his Lipschitz selection method.