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We prove the validity of maximum principles for a class of fully nonlinearoperators on unbounded subdomains $\Omega \subset \mathbb R^n$ of cylindricaltype. The main structural assumption is the uniform ellipticity of the operatoralong the bounded directions of $\Omega$, with possible degeneracy along theunbounded directions.

Directional ellipticity on special domains: weak Maximum and Phragm\`en-Lindel\"of principles