Non-local approximation of free-discontinuity problems with linear growth

Luca Lussardi; Enrico Vitali

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

  • Volume: 13, Issue: 1, page 135-162
  • ISSN: 1292-8119

Abstract

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We approximate, in the sense of Γ-convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.

How to cite

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Lussardi, Luca, and Vitali, Enrico. "Non-local approximation of free-discontinuity problems with linear growth." ESAIM: Control, Optimisation and Calculus of Variations 13.1 (2007): 135-162. <http://eudml.org/doc/249997>.

@article{Lussardi2007,
abstract = { We approximate, in the sense of Γ-convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case. },
author = {Lussardi, Luca, Vitali, Enrico},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Variational approximation; free discontinuities.; variational approximation; free discontinuities},
language = {eng},
month = {2},
number = {1},
pages = {135-162},
publisher = {EDP Sciences},
title = {Non-local approximation of free-discontinuity problems with linear growth},
url = {http://eudml.org/doc/249997},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Lussardi, Luca
AU - Vitali, Enrico
TI - Non-local approximation of free-discontinuity problems with linear growth
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/2//
PB - EDP Sciences
VL - 13
IS - 1
SP - 135
EP - 162
AB - We approximate, in the sense of Γ-convergence, free-discontinuity functionals with linear growth in the gradient by a sequence of non-local integral functionals depending on the average of the gradients on small balls. The result extends to higher dimension what we already proved in the one-dimensional case.
LA - eng
KW - Variational approximation; free discontinuities.; variational approximation; free discontinuities
UR - http://eudml.org/doc/249997
ER -

References

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