On the existence of foliations by solutions to the exterior Dirichlet problem for the minimal surface equation
Arì Aiolfi, Bustos, Daniel, Jaime Ripoll · arXiv (Cornell University) · 2020
Given an exterior domain $Ω$ with $C^{2,α}$ boundary in $\mathbb{R}^{n}$, $n\geq3$, we obtain a $1$-parameter family $u_γ\in C^{\infty}\left(Ω\right) $, $\left\vert γ\right\vert \leqπ/2$, of solutions of the minimal surface equation such that, if $\left\vert γ\right\vert