Removable sets for continuous solutions of quasilinear elliptic equations with nonlinear source or absorption terms

Abstract

This paper establishes removable singularity theorems for nonnegative continuous solutions of quasilinear elliptic equations with nonlinear source or absorption terms when an exceptional set is conditioned in terms of the regularity of Hausdorff measure and a uniform Minkowski property. These weaker conditions enable us to consider some fractal sets as an exceptional set.