We prove that special functions of bounded deformation with small jump set are close in energy to functions which are smooth in a slightly smaller domain. This permits to generalize the decay estimate by De Giorgi, Carriero, and Leaci to the linearized context in dimension n and to establish the closedness of the jump set for local minimizers of the Griffith energy.
Publié le : 2019-07-04
Classification:
functions with bounded deformation,
free discontinuity problems,
strong solutions,
Brittle fracture,
MSC 2010: 49Q20 26A45 74R10 74G65,
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA],
[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph]
@article{hal-01610691,
author = {Chambolle, Antonin and Conti, Sergio and Iurlano, Flaviana},
title = {Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy},
journal = {HAL},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01610691}
}
Chambolle, Antonin; Conti, Sergio; Iurlano, Flaviana. Approximation of functions with small jump sets and existence of strong minimizers of Griffith's energy. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-01610691/