The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity

Jarosław L. Bojarski

Applicationes Mathematicae (2005)

  • Volume: 32, Issue: 4, page 443-464
  • ISSN: 1233-7234

Abstract

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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.

How to cite

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Jarosław L. Bojarski. "The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity." Applicationes Mathematicae 32.4 (2005): 443-464. <http://eudml.org/doc/279593>.

@article{JarosławL2005,
abstract = {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.},
author = {Jarosław L. Bojarski},
journal = {Applicationes Mathematicae},
keywords = {nonlinear elasticity; lower semicontinuous relaxation of a polyconvex functional; Signorini problem; Winkler unilateral contact condition; variations},
language = {eng},
number = {4},
pages = {443-464},
title = {The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity},
url = {http://eudml.org/doc/279593},
volume = {32},
year = {2005},
}

TY - JOUR
AU - Jarosław L. Bojarski
TI - The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity
JO - Applicationes Mathematicae
PY - 2005
VL - 32
IS - 4
SP - 443
EP - 464
AB - 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.
LA - eng
KW - nonlinear elasticity; lower semicontinuous relaxation of a polyconvex functional; Signorini problem; Winkler unilateral contact condition; variations
UR - http://eudml.org/doc/279593
ER -

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