The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-6,
author = {Jaros\l aw L. Bojarski},
title = {The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity},
journal = {Applicationes Mathematicae},
volume = {32},
year = {2005},
pages = {443-464},
zbl = {1087.49012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-6}
}
Jarosław L. Bojarski. The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity. Applicationes Mathematicae, Tome 32 (2005) pp. 443-464. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am32-4-6/