Fractional differentiability for solutions of a class of parabolic systems with L1,θL1,θ-data

We study the higher differentiability of the very weak solution of the Cauchy–Dirichlet problem associated to the linear parabolic system of the form ∂u∂t−div(A(x,t)Du)=μin  Ω×]0,T[,u=0on  ∂Ω×]0,T[u=0on  Ω×{0} under a weak Hölder continuity condition on the coefficients and the right-hand side belonging to the Morrey space L1,θL1,θ. In such a way we extend to the vectorial parabolic setting the result by Di Castro and Palatucci (2013).