On differential properties of weak solutions of nonlinear elliptic systems arising in plasticity theory

In this paper local properties of weak solutions of nonlinear elliptic systems arising in problems of the deformation theory of plasticity are investigated. $L^p$-estimates are obtained for a weak solution in the case of plasticity with power-type consolidation. For linear consolidation various properties are established, such as the Hölder continuity of a weak solution, the square-integrability of its second order derivatives, and $L^p$-estimates for these derivatives. Here the elasticity and plasticity domains are introduced. In the former the solution is regular, while in the latter, when there are more than two variables, a weak solution has Hölder continuous first derivatives in a subdomain that differs from the plasticity domain by a set of measure zero.
Bibliography: 20 titles.