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This paper is divided in three parts. In the first part, we consider the functional for ai,j and Q periodic under integer translations. We assume that Q is bounded and bounded away from zero, and ai,j is a bounded elliptic matrix. We prove that there exists a universal constant M0, depending only on n, the bounds on ai,j and Q stated above, such that: given any ω ∈ Rn, there exists a class A minimizer u for the functional J for which the set {|u| < 1} is contained in the strip {x s.t. x  ω ∈ (0, M0|ω|)}. Furthermore, such u enjoys the following property of "quasi-periodicity": if ω ∈ Qn, then u is periodic (with respect to the identification induced by ω); if ω ∈ Rn − Qn, then u can be approximated uniformly on compact sets by periodic class A minimizers. The functional J introduced above has application in models for fluid jets and capillarity. In the second part of the paper, we extend the previous results to the functional

Plane-like minimizers in periodic media: jet flows and Ginzburg-Landau-type functionals