Super-linear elliptic equation for the Pucci operator without growth restrictions for the data

Esteban, Maria J.; Felmer, Patricio; Quaas, Alexander

Super-linear elliptic equation for the Pucci operator without growth restrictions for the data

Authors

Esteban, Maria J.

Felmer, Patricio

Quaas, Alexander

Description

In this paper we deal with existence and uniqueness of solution to super-linear problems for the Pucci operator: $$ -\M^+(D^2u)+|u|^{s-1}u=f(x) \quad {in} \RR^n, $$ where $s>1$ and $f$ satisfies only local integrability conditions. This result is well known when, instead of the Pucci operator, the Laplacian or a divergence form operator is considered. Our existence results use the Alexandroff-Bakelman-Pucci inequality since we cannot use any variational formulation. For radially symmetric $f$ we can prove our results under less local integrability assumptions, taking advantage of an appropriate variational formulation. We also obtain an existence result with boundary explosion in smooth domains.