Potenza : Universita degli Studi della Basilicata, Dipartimento di matematica, 2003-
Abstract
The aim of this Note is to review some recent research on viscosity solutions of
fully nonlinear equations of the form
F
x; u(x);Du(x);D2u(x)
= 0 ; x 2
where
is an open set in IRN and F is a nonlinear function of its entries which
is elliptic with respect to the Hessian matrix D2u of the unknown function u and
satises some suitable structure condition. The main issues touched here are the
Alexandrov-Bakelman-Pucci estimate, the weak Maximum Principle for bounded
solutions in general unbounded domains and qualitative Phragmen-Lindel of type
theorems
