| Issue |
ESAIM: COCV
Volume 14, Number 3, July-September 2008
|
|
|---|---|---|
| Page(s) | 456 - 477 | |
| DOI | https://doi.org/10.1051/cocv:2007061 | |
| Published online | 21 November 2007 | |
Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands
1
Dipartimento di Metodi e Modelli Matematici,
Università di Roma “La Sapienza”,
Via A. Scarpa 16, 00161 Roma, Italy; amar@dmmm.uniroma1.it; decicco@dmmm.uniroma1.it
2
Dipartimento di Matematica e Applicazioni,
Università di Napoli “Federico II”,
Complesso di Monte Sant'Angelo, Via Cintia, 80126 Napoli, Italy; nicola.fusco@unina.it
Received:
20
October
2006
Revised:
11
January
2007
New L1-lower semicontinuity and relaxation results for integral functionals defined in BV(Ω) are proved, under a very weak dependence of the integrand with respect to the spatial variable x. More precisely, only the lower semicontinuity in the sense of the 1-capacity is assumed in order to obtain the lower semicontinuity of the functional. This condition is satisfied, for instance, by the lower approximate limit of the integrand, if it is BV with respect to x. Under this further BV dependence, a representation formula for the relaxed functional is also obtained.
Mathematics Subject Classification: 49J45 / 49Q20 / 49M20
Key words: Semicontinuity / relaxation / BV functions / capacity
© EDP Sciences, SMAI, 2007
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