The Dirichlet problem for the minimal surface equation on unbounded helicoidal domains of ℝ^m

2023/06/17 by Aiolfi, Ari, Assmann, Caroline, Ripoll, Jaime
#53A10 #58J05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.10391

Abstract

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

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