Directional ellipticity on special domains: weak Maximum and Phragmèn-Lindelöf principles

Abstract

We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $\Omega \subset {\mathbb{R}}^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along the bounded directions of $\Omega$, with possible degeneracy along the unbounded directions.

20 pages, 2 figures