In this work the author deals with some very important problems in the calculus of variations related to the functional| that can be considered as the natural extension to BV(Ω) of the functional f(x,u,Du)dx, u ∈ W1,1(Ω) [see G. Dal Maso, Manuscripta Math. 30 (1979/80), no. 4, 387–416; MR0567216]. The author generalizes her results from another paper [Boll. Un. Mat. Ital. B (7) 5 (1991), no. 2, 291–313] and proves that F is lower semicontinuous, along sequences bounded in BV(Ω), relative to the strong topology of L1(Ω). The interest of the result is based on two facts: (i) the integrand f(x,s,p) is dependent on x, while in the above-mentioned paper by the author it was not so; (ii) the integrand f (x, s, p), which was supposed in Dal Maso’s paper [op. cit.] to be lower semicontinous relative to s, is not so in the present paper.
A lower semicontinuity result for functionals on BV / DE CICCO, Virginia. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - (1990).
A lower semicontinuity result for functionals on BV.
De Cicco Virginia
1990
Abstract
In this work the author deals with some very important problems in the calculus of variations related to the functional| that can be considered as the natural extension to BV(Ω) of the functional f(x,u,Du)dx, u ∈ W1,1(Ω) [see G. Dal Maso, Manuscripta Math. 30 (1979/80), no. 4, 387–416; MR0567216]. The author generalizes her results from another paper [Boll. Un. Mat. Ital. B (7) 5 (1991), no. 2, 291–313] and proves that F is lower semicontinuous, along sequences bounded in BV(Ω), relative to the strong topology of L1(Ω). The interest of the result is based on two facts: (i) the integrand f(x,s,p) is dependent on x, while in the above-mentioned paper by the author it was not so; (ii) the integrand f (x, s, p), which was supposed in Dal Maso’s paper [op. cit.] to be lower semicontinous relative to s, is not so in the present paper.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
