On removable singular sets for solutions of higher order differential inequalities

Abstract

We obtain conditions guaranteeing that weak solutions of higher order differential inequalities have a removable singularity on a compact set. These conditions depend on the fractal dimension of the singular set. For solutions of the nonlinear Poisson equation in the case of an isolated singularity, i.e. in the case where the fractal dimension of the singular set is equal to zero, they coincide with the well-known Brezis-Véron condition.