Local H 1 -regularity and H 1/3−δ -regularity up to the boundary in time dependent viscoplasticity

Abstract

Local and boundary regularity for quasistatic initial-boundary value problems from viscoplasticity is studied. The problems considered belong to a general class with monotone constitutive equations modelling materials showing kinematic hardening. A standard example is the Melan–Prager model. It is shown that the strain/stress/internal variable fields have the regularity H^4/3−δ/H^1/3−δ/H^1/3−δ up to the boundary. The proof uses perturbation estimates for monotone operator equations.