Free-boundary regularity for a problem arising in superconductivity

被引：12

作者：

Caffarelli, L ^{[1
]}

Salazar, J

Shahgholian, H

机构：

[1] Univ Texas, Dept Math, Austin, TX 78712 USA

[2] Univ Magdeburg, IAN, D-39106 Magdeburg, Germany

[3] CMAF, P-1600 Lisbon, Portugal

[4] KTH, Dept Math, S-10044 Stockholm, Sweden

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2004年 / 171卷 / 01期

关键词：

D O I：

10.1007/s00205-003-0287-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：115 / 128

页数：14

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