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ENERGY CONCENTRATION PROPERTIES OF A p-GINZBURG–LANDAU MODEL

Part of: Equations of mathematical physics and other areas of application Optimality conditions Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  25 August 2021

YUTIAN LEI Open the ORCID record for YUTIAN LEI [Opens in a new window]
YUTIAN LEI*
Affiliation:
Jiangsu Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing, 210023, China leiyutian@njnu.edu.cn
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Abstract

This paper is concerned with the p-Ginzburg–Landau (p-GL) type model with $p\neq 2$ . First, we obtain global energy estimates and energy concentration properties by the singularity analysis. Next, we give a decay rate of $1-|u_\varepsilon |$ in the domain away from the singularities when $\varepsilon \to 0$ , where $u_\varepsilon $ is a minimizer of p-GL functional with $p \in (1,2)$ . Finally, we obtain a Liouville theorem for the finite energy solutions of the p-GL equation on $\mathbb {R}^2$ .

MSC classification

Primary: 35Q56: Ginzburg-Landau equations
Secondary: 49K20: Problems involving partial differential equations 58E20: Harmonic maps , etc.
Type
Article
Information
Nagoya Mathematical Journal , Volume 247 , September 2022 , pp. 494 - 515
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Copyright
© (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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