Estimate of the Hausdorff Measure of the Singular Set of a Solution for a Semi-linear Elliptic Equation Associated with Superconductivity
نویسندگان
چکیده
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 Rn. 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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