The Filippov-Wazewski relaxation theorem revisited
type: Item
instance of: scholarly article
title: The Filippov-Wazewski relaxation theorem revisited
zbMATH Open document ID: 0930.34008
DOI: 10.1023/A:1006679923121
published in: Acta Mathematica Hungarica
publication date: 1999-10-31T00:00:00Z
review text: The authors deal with the Filippov-Wazewski relaxation theorem which states that the solution set to a Lipschitzian differential inclusion is dense in the set of relaxation solutions. Given a differential inclusion with convex-valued right-hand side the authors study the smaller set-valued map which yields the same attainable sets and, by examining the contingent derivative, they show that such a smaller set necessarily contains all the extremal points of the convex-valued map. This means that two differential inclusions have the same closure of their solution sets if and only if the right side have the same convex hull and therefore, in a certain sense, a converse of the previous relaxation theorem holds.
reviewed by: Elvira Mascolo
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49K24
zbMATH DE Number: 1355145
zbMATH Keywords: Lipschitzian differential inclusion
author: I. Joó
author: Péter Tallos
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1355145