Regularity for degenerate elliptic and parabolic systems

In this work local behavior for solutions to the inhomogeneous
p-Laplace in divergence form and its parabolic version are studied.
It is parabolic and non-linear generalization of the
Calderon-Zygmund theory for the Laplace operator. I.e. the
borderline case BMO is studied. The two main results are local BMO
and Hoelder estimates for the inhomogenious p-Laplace and the
parabolic p-Laplace system. An adaption of some estimates to fluid
mechanics, namely on the p-Stokes equation are also proven. The
p-Stokes system is a very important physical model for so-called
non Newtonian fluids (e.g. blood). For this system BMO and Hoelder
estimates are proven in the stationary 2-dimensional case.