Elliptic and Parabolic Equations - Abstract

Knees, Dorothee

On global spatial regularity in elasto-plasticity

In the lecture we present a spatial regularity result for solutions of evolution models from small-strain elasto-plasticity with linear hardening (e.g. with kinematic hardening). While the existence theory for such models is well established, the investigation of the regularity properties is an active field of research. In the lecture we focus on higher spatial regularity in Sobolev--Slobodeckij spaces. Under natural assumptions on the data we show for domains with smooth boundaries that the displacement fields belong to $L^infty((0,T);H^frac32-delta(Omega))$ (globally) and that the inner variables (plastic strain, hardening variables) belong to $L^infty((0,T);H^frac12-delta(Omega))$ for every $delta>0$. The results are obtained by combining estimates for difference quotients with a reflection argument. Finally we discuss the implication of the results on the convergence rates of numerical schemes.