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Regularity in parabolic Dini continuous systems

Abstract We consider a weak solution to the non-linear, parabolic systems of the form ut – div A(x, t, u, Du) = 0, where the vector field A satisfies a Dini-type continuity condition with respect to the variables (x, t, u), and we prove a partial regularity result for such a solution. Moreover, we give an estimate of the size of the singular set of a solution in terms of a generalized parabolic Hausdorff measure associated to an appropriate modulus of continuity naturally associated to the coefficients of the system.