Electronic properties of superconductor-semiconductor mesoscopic device.
Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity
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 . 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 -rectifiable. In this paper, we shall show that under some additive smoothness assumptions, the -dimensional Hausdorff measure of singular set...
Existence of weak solutions to a class of degenerate semiconductor equations modeling avalanche generation.