THE REMOVABLE SINGULARITY THEOREM FOR HARMONIC FUNCTION ON A TWO-DIMENSIONAL STRATIFIED SET

We prove the removable singularity theorem for harmonic function on a two-dimensional stratified set. It is shown that harmonic and bounded function defined on the twodimensional stratified set, except the zero-dimensional strata, is harmonic extendable over all stratified set. This theorem plays an important role in the proof of the solvability of the Dirichlet problem for the Laplace equation on stratified set and in the implement of Poincar-Perron method on a stratified set. In proof we use analogues of divergence theorem and Harnack’s inequality on a stratified set. We provide basic information from the theory of differential equations on the stratified sets, which are necessary for the formulation and proof of main result.

stratified set, removable singularity theorem, harmonic function