A new space of generalised functions with bounded variation motivated by fracture mechanics

We introduce a new space of generalised functions with bounded variation to prove the existence of a solution to a minimum problem that arises in the variational approach to fracture mechanics in elastoplastic materials. We study the fine properties of the functions belonging to this space and prove...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Nonlinear differential equations and applications 2022-11, Vol.29 (6), Article 63
Hauptverfasser: Dal Maso, Gianni, Toader, Rodica
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We introduce a new space of generalised functions with bounded variation to prove the existence of a solution to a minimum problem that arises in the variational approach to fracture mechanics in elastoplastic materials. We study the fine properties of the functions belonging to this space and prove a compactness result. In order to use the Direct Method of the Calculus of Variations we prove a lower semicontinuity result for the functional occurring in this minimum problem. Moreover, we adapt a nontrivial argument introduced by Friedrich to show that every minimizing sequence can be modified to obtain a new minimizing sequence that satisfies the hypotheses of our compactness result.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-022-00793-0