Filippov’s Theorem for mutational inclusions in a metric space

• Verfasst von: Frankowska, Halina [VerfasserIn]
• Verfasst von: Lorenz, Thomas [VerfasserIn]
• Titel: Filippov’s Theorem for mutational inclusions in a metric space
• Verf.angabe: Hélène Frankowska and Thomas Lorenz
• Jahr: 2023
• Umfang: 42 S.
• Fussnoten: Veröffentlicht: 26. Jun 26, 2023 ; Gesehen am 28.09.2023
• Titel Quelle: Enthalten in: Scuola Normale Superiore di Pisa. Classe di ScienzeAnnali della Scuola Normale Superiore di Pisa, Classe di Scienze
• Ort Quelle: Pisa : Scuola Normale Superiore, 1871
• Jahr Quelle: 2023
• Band/Heft Quelle: 24(2023), 2, Seite 1053-1094
• ISSN Quelle: 2036-2145
• DOI: doi:10.2422/2036-2145.202106_009
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1860466079

Abstract

This article is devoted to an extension of the celebrated Filippov theorem to the metric space setting. We deal with fairly general metric spaces, where derivatives of time-dependent functions are replaced by mutations and solutions of differential equations/inclusions are mutational primitives of (time-dependent) maps of transitions. As an example of application we discuss measure-valued solutions to a controlled transport equation and state the Filippov theorem in this context. We also show that whenever a transport equation is generated by Lipschitz vector fields its classical weak solutions coincide with its mutational solutions. Our abstract setting applies as well to systems on the space of nonempty compact subsets of Rn endowed with the Pompeiu-Hausdorff distance and to continuity equations/inclusions on Wasserstein spaces of Borel probability measures.