The dirichlet problem for the minimal surface equation on unbounded helicoidal domains of Rm

Abstract

We consider a helicoidal group G in R n+1 and unbounded Ginvariant C 2,α-domains Ω ⊂ R n+1 whose helicoidal projections are exterior domains in R n, n ≥ 2. We show that for all s ∈ R, there exists a G-invariant solution us ∈ C 2,α Ω of the Dirichlet problem for the minimal surface equation with zero boundary data which satisfies sup∂Ω |grad us| = |s|. Additionally, we provide further information on the behavior of these solutions at infinity.