Regularity of solutions to coercive and self-controlling viscoplastic problems

We prove higher regularity of solutions to viscoplastic problems. The main idea is to use the finite difference method, which allows us to cancel the monotone nonlinearities. Our main assumption is that velocity is in L 2 ( H 1 ) . This is true for all coercive and some special (for example linear self-controlling) non-coercive models.