Regularity in parabolic Dini continuous systems
Paolo Baroni · Forum Mathematicum · 2010
Abstract We consider a weak solution to the non-linear, parabolic systems of the form u t – 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.