In this paper, we study the infinity harmonic functions with linear growth rate at infinity defined on exterior domains. We show that such functions must be asymptotic to planes or cones at infinity. We also establish the solvability of Dirichlet problems for exterior domains.

中文翻译：

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外域上的无穷谐函数

在本文中，我们研究了在外部域上定义的在无穷远处具有线性增长率的无穷远调和函数。我们证明这些函数必须在无穷远处渐近于平面或锥体。我们还建立了外部域 Dirichlet 问题的可解性。