Characterization of Filippov representable maps and Clarke subdifferentials
成果类型：
Article
署名作者：
Bivas, Mira; Daniilidis, Aris; Quincampoix, Marc
署名单位：
University of Sofia; Bulgarian Academy of Sciences; Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bretagne Occidentale
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-020-01540-y
发表日期：
2021
页码：
99-115
关键词：
摘要：
The ordinary differential equation (x) over dot(t) = f (x(t)), t >= 0, for f measurable, is not sufficiently regular to guarantee existence of solutions. To remedy this we may relax the problem by replacing the function f with its Filippov regularization F-f and consider the differential inclusion (x) over dot(t) is an element of F-f (x(t)) which always has a solution. It is interesting to know, inversely, when a set-valued map Phi can be obtained as the Filippov regularization of a (single-valued, measurable) function. In this work we give a full characterization of such set-valued maps, hereby called Filippov representable. This characterization also yields an elegant description of those maps that are Clarke subdifferentials of a Lipschitz function.
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