Full regularity for a class of degenerated parabolic systems in two spatial variables

The authors consider quasilinear parabolic systems partial derivative(t)u - div a(del u) = 0 in two space dimensions. The function a has p-growth behaviour, 1 < p < inf inity, and the ellipticity "constant" behaves like (1 + \del u\)(P-2). The author prove full regularity of the weak solution on interior subdomains, b ut globally in time. The key idea in the proof is a technique to obtain bou ndedness of the gradient based on logarithmic estimates.