Stable and singular solutions of the equation $Delta u = 1/u$ Alexander Meadows We study properties of the semilinear elliptic equation $\Delta u = 1/u$ on domains in $\mathbb{R}^{n}$, with an eye toward nonnegative singular solutions as limits of positive smooth solutions. We prove the nonexistence of such solutions in low dimensions when we also require them to be stable for the corresponding variational problem. The problem of finding singular solutions is related to the general study of singularities of minimal hypersurfaces of Euclidean space. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2560 10.1512/iumj.2004.53.2560 en Indiana Univ. Math. J. 53 (2004) 1683 - 1706 state-of-the-art mathematics http://iumj.org/access/