Variational characterization of interior interfaces in phase transition models on convex plane domains.

Garza-Hume, Clara E.; Padilla, Pablo

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We construct geometric barriers for minimal graphs in $ℍ^{n} \times ℝ .$ We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in $ℍ^{n}$ extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces. In $ℍ^{n} \times ℝ$ , we solve the Dirichlet problem for the vertical minimal equation in a $C^{0}$ convex domain $Ω \subset ℍ^{n}$ taking arbitrarily continuous...