Parabolic systems with non continuous coefficients (Q1422585)

The author studies the local regularity of the solutions of the following parabolic system \[ u_t= \sum^N_{j=1} \sum_{|\alpha|= 2s} a^{(2)}_{ij}(y) D^\alpha u_j(y) \sum^N_{j=1} \sum_{|\alpha|\leq 2s-1} b^{(2)}_{ij}(y) D^2 u_j(y)+ f_i(y)\tag{1} \] for \(i= 1,\dots, N\). She obtains the \(L^p\) estimates for solutions of (1) with discontinuous coefficients for every \(1< p<\infty\).