On the existence of foliations by solutions to the exterior Dirichlet problem for the minimal surface equation

Ari Aiolfi, Daniel Bustos, Jaime Ripoll

Given an exterior domain $\Omega$ with $C^{2,\alpha }$ boundary in ${\mathbb{R}}^n$, $n\ge 3$, we obtain a $1$-parameter family $u_{\gamma }\in C^{\infty }\left(\Omega \right)$, $\left\vert γ\right\vert \l…