Ricerc@Sapienza

This paper is divided in two parts: the first one is a survey about recent results on the regularizing effect of lower order terms on solutions of nonlinear Dirichlet problems; in the second part we prove two existence theorems (related to the results of the first part) concerning elliptic systems.

In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies - Δ u = f (u) in B1, where u ∈ C2 (B1), B1 is the unit ball of R2 and f is a smooth nonlinearity. Other results on the nondegeneracy of the critical points and the shape of the level sets are proved.

This book is the reprint of the 1998 edition of Elliptic Partial Differential Equations of Second Order by David Gilbarg and Neil S. Trudinger that originally appeared in 1977.