# Article

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Keywords:
singular set; semi-linear elliptic equation; Ginzburg-Landau system
Summary:
We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space \${\mathbb{R}}^n\$. In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is \$(n-2)\$-rectifiable. In this paper, we shall show that under some additive smoothness assumptions, the \$(n-2) \$-dimensional Hausdorff measure of singular set of any solution is locally finite.
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