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.
On the weak maximum principle for fully nonlinear elliptic pde's in general unbounded domains / CAPUZZO DOLCETTA, Italo. - In: LECTURE NOTES OF SEMINARIO INTERDISCIPLINARE DI MATEMATICA. - ISSN 2284-0206. - 7:(2008), pp. 81-92.
On the weak maximum principle for fully nonlinear elliptic pde's in general unbounded domains
CAPUZZO DOLCETTA, Italo
2008
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
