*Published Paper*

**Inserted:** 6 oct 2012

**Last Updated:** 6 oct 2012

**Journal:** Forum Math.

**Volume:** 23

**Number:** 6

**Pages:** 1281-1322

**Year:** 2011

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**Abstract:**

We consider a weak solution to the non-linear, parabolic systems $u_t-\text{div} \,A(x,t,u,Du)=0$, 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.

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