Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains

Abstract EN

We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term.

We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary.

As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem.