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Degenerate elliptic systems and applications to Ginzburg-Landau type equations, part I

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Abstract

This paper has three topics. In Sect. 1, we present our results on the regularity and a priori estimates for solutions ofp-harmonic systems with Hölder continuous coefficients. Such systems come up in the study of Ginzburg-Landau type functional in higher dimensions. In Sect. 2, we study a stability inequality, which, in addition to its applications in the study of Ginzburg-Landau type functional, is of independent interest. In Sects. 3 and 4, we prove that for any sequence of minimizers of the higher dimensional Ginzburg-Landau type functional, a subsequence converges strongly away from a finite number of points, generalizing some of the two dimensional results of Bethuel, Brezis, and Hélein.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Zheng -Chao Han & Yan Yan Li

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  1. Zheng -Chao Han
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  2. Yan Yan Li
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Partially supported by the Alfred P. Sloan Foundation Research Fellowship and NSF grant DMS-9401815.

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Han, Z.C., Li, Y.Y. Degenerate elliptic systems and applications to Ginzburg-Landau type equations, part I. Calc. Var 4, 171–202 (1996). https://doi.org/10.1007/BF01189953

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