On removable singular sets for solutions of higher order differential inequalities

Abstract

We obtain conditions guaranteeing that weak solutions of the differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge f (x) g (|u|) \quad \mbox{in } \Omega \setminus S, $$ has a removable singular set $S \subset \Omega$, where $\Omega$ is a bounded domain and $a_\alpha$, $f$, and $g$ are some functions.