On a necessary condition for removing singularities of solutions of nonlinear elliptic inequalities

Abstract

We study solutions of the differential inequality $$ Δ^{m / 2} u \ge f (x) g (u) \quad \mbox{in } B_1 \setminus \{ 0 \}, $$ where $m \ge 2$ is an even integer, $f$ and $g$ are some functions, and $B_1$ is an open unit ball in $R^n$, $n \ge 2$, centered at zero. Our aim is to obtain a necessary condition for a singularity at zero to be removable for any solution of this inequality.