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

G. A. Seregin

Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 289-309

Résumé

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.