Regularity for minimaizers of some variational problems in plasticity theory

A variational problem for functionals depending on the symmetric part of the gradient of unknown vector-valued function is considered. We suppose that the integrand of the problem has the power growth with the exponent less then two. We prove summability of the second derivatives of minimizers near the boundary. In two-dimentional case Hölder continuity up to the boundary of the strain and stress tensors is established.