Global spatial regularity for time dependent elasto-plasticity and related problems

Abstract

We study the global spatial regularity of solutions of generalized elasto-plastic models with linear hardening on smooth domains. Under natural smoothness assumptions on the data and the boundary we obtain that the displacements belong to L^8((0,T);H^(3/2-d)(O)) whereas the internal variables belong to L^8((0,T);H^(1/2-d)(O)). The key step in the proof is a reflection argument which gives the regularity result in directions normal to the boundary on the basis of tangential regularity results