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32,4 (2005), pp. 443 464 Jarosław L. Bojarski (Warszawa) THE RELAXATION OF THE SIGNORINI PROBLEM FOR POLYCONVEX FUNCTIONALS WITH LINEAR GROWTH AT INFINITY Abstra t. The aim of this paper is to study the unilateral onta t ondition (Signorini problem) for poly onvex fun tionals with linear growth at in nity. We nd the lower semi ontinuous relaxation of the original fun tional (de ned over a subset of the spa e of bounded variations BV (Ω)) and we prove the existen e theorem. Moreover, we dis uss the Winkler unilateral onta t ondition. As an appli ation, we show a few examples of elasti -plasti potentials for nite displa ements. 1. Introdu tion. Let Ω be a bounded, open, onne ted set of lass C1 in R3. The aim of this paper is to study the poly onvex fun tional (1.1) u 7→ \

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