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.

A new space of generalised functions with bounded variation motivated by fracture mechanics / Dal Maso, G.; Toader, R.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 29:6(2022), pp. 1-35. [10.1007/s00030-022-00793-0]

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

Dal Maso G.;Toader R.
2022-01-01

Abstract

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.
2022
29
6
1
35
63
Dal Maso, G.; Toader, R.
File in questo prodotto:
File Dimensione Formato  
DM-Toa-22-01-10-sissa.pdf

non disponibili

Descrizione: preprint
Tipologia: Documento in Pre-print
Licenza: Non specificato
Dimensione 403.04 kB
Formato Adobe PDF
403.04 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/138151
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact