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Minimal Graphs in n × and n + 1

Ricardo EarpEric Toubiana — 2010

Annales de l’institut Fourier

We construct geometric barriers for minimal graphs in n × . We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in 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 n × , we solve the Dirichlet problem for the vertical minimal equation in a C 0 convex domain Ω n taking arbitrarily continuous finite boundary...

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