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On a quasilinear system arising in the theory of superconductivity

Published online by Cambridge University Press:  04 April 2011

Gary Lieberman  and
Xing-Bin Pan
Gary Lieberman
Affiliation:
Department of Mathematics, Iowa State University, Ames, IA 50011, [email protected]
Xing-Bin Pan
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of [email protected]
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Abstract

We examine the regularity of the solution of a quasilinear system involving the curl of vector fields. This system arises in the mathematical theory of superconductivity. The C2+α regularity was obtained by Bates and Pan under the condition that Ω is simply connected and has no holes, and that the normal component of the curl of the boundary data vanishes. The aim of this paper is to remove these technical restrictions on the topology of the domain and on the boundary data. By carefully studying the related quasilinear Neumann problem, we obtain the C2+α regularity without assuming these technical conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 2 , April 2011 , pp. 397 - 407
Copyright
Copyright © Royal Society of Edinburgh 2011

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