# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Regularity of solutions in plasticity. I: Continuum

### Tom 30 / 2003

Applicationes Mathematicae 30 (2003), 337-364 MSC: Primary 49N60; Secondary 49J45, 49K30, 74C05. DOI: 10.4064/am30-3-8

#### Streszczenie

The aim of this paper is to study the problem of regularity of solutions in Hencky plasticity. We consider a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space $LD({\mit\Omega}) \equiv \{% {\bf u}\in L^{1}({\mit\Omega},{\Bbb R}^{n})\mid\nabla {\bf u}+(\nabla {\bf u})^{T}\in L^{1}({\mit\Omega},{\Bbb R}^{n\times n})\}$ if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.

#### Autorzy

• Jarosław L. BojarskiInstitute of Fundamental Technological Research