Precise Morrey regularity of the weak solutions to a kind of quasilinear systems with discontinuous data

We consider the Dirichlet problem for a class of quasilinear elliptic systems in domain with irregular boundary. The principal part satisfies componentwise coercivity condition and the nonlinear terms are Carathéodory maps having Morrey regularity in x and verifying controlled growth conditions with respect to the other variables. We have obtained boundedness of the weak solution to the problem that permits to apply an iteration procedure in order to find optimal Morrey regularity of its gradient.

Consideriamo il problema di Cauchy-Dirichlet per una classe di sistemi quasilineari elliuttici in dominii con frontiera irregolare.La parte principale soddisfa la condizione di corcitività componrnte per componente