For the analysis of strongly coupled material models it is useful to have
deeper insight into the spatial regularity properties of the involved
quantities like displacement fields or internal variables.
In this lecture we will discuss some recent results for non-smooth
situations with a special focus on  certain rate-independent damage models
in the small strain regime and Tresca friction models along cracks .
The talk relies on joint results with R. Rossi (University of Brescia), C.
Zanini (Politecnico di Torino) and A. Schroeder (University of Salzburg).