Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity

Junichi Aramaki

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 3, page 185-201
  • ISSN: 0044-8753

Abstract

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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 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.

How to cite

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Aramaki, Junichi. "Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity." Archivum Mathematicum 046.3 (2010): 185-201. <http://eudml.org/doc/116482>.

@article{Aramaki2010,
abstract = {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.},
author = {Aramaki, Junichi},
journal = {Archivum Mathematicum},
keywords = {singular set; semi-linear elliptic equation; Ginzburg-Landau system; singular set; semi-linear elliptic equation; Ginzburg-Landau system},
language = {eng},
number = {3},
pages = {185-201},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity},
url = {http://eudml.org/doc/116482},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Aramaki, Junichi
TI - Estimate of the Hausdorff measure of the singular set of a solution for a semi-linear elliptic equation associated with superconductivity
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 3
SP - 185
EP - 201
AB - 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.
LA - eng
KW - singular set; semi-linear elliptic equation; Ginzburg-Landau system; singular set; semi-linear elliptic equation; Ginzburg-Landau system
UR - http://eudml.org/doc/116482
ER -

References

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