On global spatial regularity in elasto-plasticity with linear hardening

We study the global spatial regularity of solutions of elasto-plastic models with linear hardening. In order to point out the main idea, we consider a model problem on a cube, where we prescribe Dirichlet and Neumann boundary conditions on the top and the bottom, respectively, and periodic boundary conditions on the remaining faces. Under natural smoothness assumptions on the data we obtain u is an element of L(infinity) ((0, T); H(3/2-delta)(Omega)) for the displacements and z is an element of L(infinity) ((0, T); H(1/2-delta)(Omega)) for the internal variables. The proof is based on a difference quotient technique and a reflection argument.