We study the regularity of weak solutions to a class of second order parabolic system under only the assumption of continuous coefficients. We prove that the weak solution u to such system is locally Hölder continuous with any exponent α ∈ (0, 1) outside a singular set with zero parabolic measure. In particular, we prove that the regularity point in Q_T is an open set with full measure, and we obtain a general criterion for the weak solution to be regular in the neighborhood of a given point. Finally, we deduce the fractional time and fractional space differentiability of Du, and at this stage, we obtain the Hausdorff dimension of a singular set of u.

我们研究了仅在连续系数假设下一类二阶抛物线系统弱解的规律性。我们证明了这种系统的弱解u是局部 Hölder 连续的，并且具有零抛物线测度的奇异集之外的任何指数α ∈ (0, 1)。特别地，我们证明了Q _T中的正则点是一个全测度的开集，并且我们得到了弱解在给定点的邻域内是正则的一般准则。最后，我们推导了Du的分数时间和分数空间可微性，在这个阶段，我们得到了u的奇异集的Hausdorff 维数。