Symmetric solutions of the singular minimal surface equation (Q2042116)

This nice paper investigates all rotational symmetric solutions \(u\) on a give open set \(\Omega\subset\mathbb R^n\) to the symmetric minimal surface equation \[ \hbox{div}\Bigg(\frac{Du}{\sqrt{1+|Du|^2}}\Bigg)=\frac{\alpha}{u\sqrt{1+|Du|^2}} \] Since the case \(\alpha=0\) of the last equation is the classical minimal surface equation, the results obtained in this paper are classified according to \(\alpha<0\) (Theorem 1) and \(\alpha>0\) (Theorem 7). Moreover, some interesting geometric-analytic properties of the solutions are presented in Theorems 13, 14, 17, 19, 20.