Regularity results for solutions of a class of parabolic systems with measure data (Q412668)

The paper deals with the following Cauchy-Dirichlet problem associated to linear uniformly parabolic systems of the form NEWLINE\[NEWLINE \begin{cases} {{\partial u}\over {\partial t}}-\text{div\,}\big(A(x,t)Du\big)=\mu & \text{in}\;\Omega\times(0,T),\\ u=0 & \text{on}\;\partial\Omega\times(0,T),\\ u=0 & \text{in}\;\Omega\times\{0\}, \end{cases} NEWLINE\]NEWLINE where \(\Omega\) is a \(C^1\)-smooth domain, the coefficients belong to \(L^\infty\cap VMO\) and \(\mu\) is a measure in \(L^1.\) The authors prove existence, uniqueness and regularity in Morrey spaces of a suitably defined solution of Stampacchia type to the above system. Moreover, it is shown that the Morrey regularity of the gradient improves when \(\mu\in L^{1,\tau}\).