On removable singular sets for solutions of higher order differential inequalities

Abstract

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