Lipschitz Kernel of a Closed Set-Valued Map |
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Authors: | Luc Doyen |
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Institution: | (1) CNRS, ERS 644, Centre de Recherche Viabilité-Contrôle, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris cedex 16, France |
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Abstract: | This paper deals with Lipschitz selections of set-valued maps with closed graphs. First, we characterize Lipschitzianity of a closed set-valued map in the differential games framework in terms of a discriminating property of its graph. This allows us to consider the -Lipschitz kernel of a given set-valued map as the largest -Lipschitz closed set-valued map contained in the initial one, to derive an algorithm to compute the collection of Lipschitz selections, and to extend the Pasch–Hausdorff envelope to set-valued maps. |
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Keywords: | Lipschitz selection Lipschitz kernel Lipschitz extension discriminating kernel |
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