Università Roma Tre

Classi theory of the Dirichlet problem: mean principle, maximum principle, Green foirmulas, Perron method, potential theory.

Sobolev spaces in one and $n$ dimensions, with the immersion theorems.

Elliptic systems of equations; weak solutions and the Lax-Milgram theorem.

Caccioppoli estimates and $W^{2,2}$ regularity of the solutions of elliptic sustems.

Maximal function of Hardy and Littlewood; a proof of the Lebesgue differentiation theorem; weak $L^p$ spaces and the Marcinkievitz interpolation theorem.

Protter-Weinberger, Maximum principles in Differential Equations.

L. V. Ahlfors, Compes Analysis.

H. Brezis, Analisi Funzionale.

M. Giaquinta, L. Martinazzi, An introduction to the regularity theory for elliptic systems, harmoinic functions and minimal graphs.