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

Volume 32 / 2005

Jarosław L. Bojarski Applicationes Mathematicae 32 (2005), 443-464 MSC: 26B30, 46A11, 47H04, 49J45, 74B20, 74C15. DOI: 10.4064/am32-4-6


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.


  • Jarosław L. BojarskiDepartment of Applied Mathematics
    Warsaw Agricultural University–SGGW
    Nowoursynowska 159
    02-787 Warszawa, Poland

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