Quasilinear systems associated with superconductivity

Abstract

In a previous article, Aramaki [4] considered a semilinear system with general nonlinearity in a three dimensional domain which arises in the mathematical theory of superconductivity. There the problem is reduced to the study of a quasilinear system. There it is assumed that the domain is simply-connected and without holes, and that the normal component of the curl of the boundary data vanishes. In this article, we these conditions are removed, and the analysis relies heavily on the recent work by Lieberman and Pan [16].

Keywords

• Quasilinear system
• superconductivity
• regularity of weak solutions