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Free-boundary regularity for a problem arising in superconductivity
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2004 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 171, no 1, 115-128 p.Article in journal (Refereed) Published
Abstract [en]

This paper concerns regularity properties of the mean-field theory of superconductivity. The problem is reminiscent of the one studied earlier by L.A. Caffarelli, L. Karp and H. Shahgholian in connection with potential theory. The difficulty introduced in this paper is the existence of several patches, where on each patch the solution to the problem may have different constant values. However, using a refined analysis, we reduce the problem to the one-patch case, at least locally near ''regular'' free boundary points. Using a monotonicity formula, due to Georg S. Weiss, we characterize global solutions of a related equation. Hence earlier regularity results apply and we conclude the C-1 regularity of the free boundary.

Place, publisher, year, edition, pages
2004. Vol. 171, no 1, 115-128 p.
Keyword [en]
obstacle problem, model
National Category
URN: urn:nbn:se:kth:diva-23040DOI: 10.1007/s00205-003-0287-0ISI: 000187502700006ScopusID: 2-s2.0-0742306184OAI: diva2:341738
QC 20100525 QC 20111101Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2011-11-01Bibliographically approved

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