Prof. Giuseppe Rosario Mingione
Dipartimento di Matematica dell'Università di Parma, Parco Area delle Scienze 53/a (Campus) 43100 Parma, Italy

Calderòn-Zygmund estimates for degenerate parabolic systems

Calderòn-Zygmund estimates allow to get information on the integrability of solutions to systems of pde, starting from that of the "data" (right hand side or boundary value, typically). These are by now classical for linear problems, while for non-linear ones, p-Laplacean equation as model, they are due more recently to Iwaniec and DiBenedetto-Manfredi. All these approaches make use of tools from harmonic analysis, such as singular integrals or maximal operators. From this very reason, parabolic systems as the one involving the evolutionary p-Laplacean operator are ruled. I will present a harmonic analysis free approach leading to a Calderòn-Zygmund theory for general non linear parabolic systems and equations.