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

Abstract

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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.

How to cite

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Amar, 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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