On removable singular sets for solutions of higher order differential inequalities

TL;DR

This paper establishes conditions under which singularities in solutions to certain higher order differential inequalities can be removed, ensuring solutions extend smoothly across singular sets.

Contribution

It provides new criteria for the removability of singular sets in solutions of higher order differential inequalities, expanding understanding of solution regularity.

Findings

Identifies conditions for removability of singular sets

Extends previous results to higher order inequalities

Provides a framework for analyzing singularities in 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.