Partial regularity and singular sets of solutions of higher order parabolic systems

In the present paper we provide a broad survey of the regularity theory for non-differentiable higher order parabolic systems of the type Initially, we prove a partial regularity result with the method of A-polycaloric approximation, which is a parabolic analogue of the harmonic approximation lemma of De Giorgi. Moreover, we prove better estimates for the maximal parabolic Hausdorff-dimension of the singular set of weak solutions, using fractional parabolic Sobolev spaces. Thereby, we also consider different situations, which yield a better dimension reduction result, including the low dimensional case and coefficients A(z, D ^m u), independent of the lower order derivatives of u.