The Dirichlet problem for the $\alpha$-singular minimal surface equation
Rafael López · arXiv (Cornell University) · 2018
Let $\Omega\subset\r^n$ be a bounded mean convex domain. If $\alpha<0$, we prove the existence and uniqueness of classical solutions of the Dirichlet problem in $\Omega$ for the $\alpha$-singular minimal surface equation with arbitrary continuous boundary data.