ON THE REGULARITY OF SETS IN RIEMANNIAN MANIFOLDS

This paper is devoted to the study of the normal (tangential) regularity of a closed set and the subdifferential (directional) regularity of its distance function in the context of Riemannian manifolds. The Clarke, Fréchet and proximal subdifferentials of the distance function from a closed subset in a Riemannian manifold are represented by corresponding normal cones of the set.

ON GLOBAL SPATIAL REGULARITY AND CONVERGENCE RATES FOR TIME-DEPENDENT ELASTO-PLASTICITY

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 u ∈ L∞((0, T); H3/2-δ(Ω)) for the displacements and z ∈ L∞((0, T); H1/2-δ(Ω)) for the internal variables. The proof relies on a reflection argument which gives the regularity result in directions normal to the boundary on the basis of tangential regularity results. Based on the regularity results we derive convergence rates for a finite element approximation of the models.