# Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands

Micol Amar; Virginia De Cicco; Nicola Fusco

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 14, Issue: 3, page 456-477
- ISSN: 1292-8119

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topAmar, Micol, De Cicco, Virginia, and Fusco, Nicola. "Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2007): 456-477. <http://eudml.org/doc/90878>.

@article{Amar2007,

abstract = {
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.
},

author = {Amar, Micol, De Cicco, Virginia, Fusco, Nicola},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Semicontinuity; relaxation; BV functions; capacity; semicontinuity},

language = {eng},

month = {11},

number = {3},

pages = {456-477},

publisher = {EDP Sciences},

title = {Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands},

url = {http://eudml.org/doc/90878},

volume = {14},

year = {2007},

}

TY - JOUR

AU - Amar, Micol

AU - De Cicco, Virginia

AU - Fusco, Nicola

TI - Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/11//

PB - EDP Sciences

VL - 14

IS - 3

SP - 456

EP - 477

AB -
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.

LA - eng

KW - Semicontinuity; relaxation; BV functions; capacity; semicontinuity

UR - http://eudml.org/doc/90878

ER -

## References

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