Uniqueness of blowup at singular points for superconductivity problem-Reference-Cited by-同舟云学术

Uniqueness of blowup at singular points for superconductivity problem

Published:2024-08-01 Issue:8 Volume:65 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Du Lili¹²,Tang Xu¹^ORCID,Wang Cong¹^ORCID

Affiliation:

1. Department of Mathematics, Sichuan University 1 , Chengdu 610064, People’s Republic of China

2. School of Mathematical Science, Shenzhen University 2 , Shenzhen 518061, People’s Republic of China

Abstract

In this paper, we investigate the uniqueness of blowup at singular points of the free boundary in the superconductivity problem. We provide a sufficient condition and demonstrate that this condition can be verified in certain special cases. The proof of the main results in this paper is primarily based on Weiss-type and Monneau-type monotonicity formulas, and is inspired by the recent paper [Chen et al. arXiv: 2204.11426v2 (2022)].

Funder

National Natural Science Foundation of China

Sichuan Provincial Youth Science and Technology Foundation

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0213622/20094460/081502_1_5.0213622.pdf

Reference18 articles.

1. A semi-elliptic system arising in the theory of type-II superconductivity;Comm. Appl. Nonlinear Anal.,1994

2. Distribution of vortices in a type-II superconductor as a free boundary problem: Existence and regularity via Nash–Moser theory;Interfaces Free Bound,2000

3. The obstacle problem revisited;J. Fourier Anal. Appl.,1998

4. Solutions of fully nonlinear elliptic equations with patches of zero gradient: Existence, regularity and convexity of level curves;Trans. Amer. Math. Soc.,2002

5. The structure of the singular set of a free boundary in potential theory;Izv. Nats. Akad. Nauk Armenii Mat.,2004