The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity
Tom 32 / 2005
Applicationes Mathematicae 32 (2005), 443-464
MSC: 26B30, 46A11, 47H04, 49J45, 74B20, 74C15.
DOI: 10.4064/am32-4-6
Streszczenie
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 $BV({\mit\Omega} )$) 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.
