Year: 2025
Type: article
Abstract: In [18], the authors introduced the space of scalar-valued functions $$GBV_\star (A)$$ G B V ⋆ ( A ) to minimise a class of functionals whose study is motivated by fracture mechanics. In this paper, we extend the definition of $$GBV_\star (A)$$ G B V ⋆ ( A ) to the vectorial case, introducing the space $$GBV_\star (A;{{\mathbb {R}}}^k)$$ G B V ⋆ ( A ; R k ) . We study the main properties of $$GBV_\star (A;{{\mathbb {R}}}^k)$$ G B V ⋆ ( A ; R k ) and prove a lower semicontinuity result useful for minimisation purposes. With the Direct Method in mind, we adapt the arguments of [18] to show that minimising sequences in $$GBV_\star (A;{{\mathbb {R}}}^k)$$ G B V ⋆ ( A ; R k ) can be modified to obtain a minimising sequence converging $${\mathcal {L}}^d$$ L d -a.e in A.
Author: Davide Donati
Institution: Scuola Internazionale Superiore di Studi Avanzati
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4410460916