Xu-Sheng Du

Symmetry, monotonicity, and asymptotics of singular solutions to semilinear elliptic equations

In this paper, we study singular positive solutions to the semilinear elliptic equation $$ - \Delta u = f(u) ~~~~~~ \textmd{in} ~ \Omega \setminus \Gamma, $$ where $\Omega \subset \R^n$ is a bounded or unbounded domain, and $\Gamma \subset \Omega$ is a singular closed set with zero Newtonian capacity. When $\Omega = \R...