On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order

We are concerned with the problem of differentiability of the derivatives of order m + 1 of solutions to the "nonlinear basic systems" of the type (-1)(m) Sigma(vertical bar alpha vertical bar=m) D-alpha A(alpha) (D((m))u) + partial derivative u/partial derivative t = 0 in Q. We are able to show that D(alpha)u is an element of L-2 (-alpha,0,H-theta (B(sigma),R-N)),R- vertical bar alpha vertical bar = m + 1, for nu is an element of (0, 1/2) and this result suggests that more regularity is not expectable.