The Dirichlet problem for the $\alpha$-singular minimal surface equation

Abstract

Let $Ω\subset\r^n$ 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.

12 pages. Accepted to be published in Archiv der Mathematik