Interior gradient bounds for nonlinear elliptic systems

Abstract

This manuscript is dedicated to Umberto Mosco, with esteem and affection. Umberto was my mentor at the University of Rome, where I completed my four years studies in Mathematics before my PhD program in Pisa. I dedicate to him the article, which is divided in two parts. In the first section I propose some regularity theorems, precisely some interior bounds for the gradient of weak solutions to a class of nonlinear elliptic systems; the title of this manuscript takes its origin from this section. The second part of the manuscript deals with my first studies in Rome together with Umberto Mosco and with my next studies in Pisa where I met Ennio De Giorgi and where I had the good fortune of assisting to the birth of the G−convergence and the Γ−convergence theories, with some connections with the Mosco’s convergence.

Keywords

• elliptic systems
• regularity of solutions
• general growth conditions
• gammaconvergence
• g-convergence
• mosco-convergence.