Global Uniform Estimate for the Modulus of Two-Dimensional Ginzburg-Landau Vortexless Solutions with Asymptotically Infinite Boundary Energy

Ignat, Radu; Kurzke, Matthias; Lamy, Xavier

Abstract

For ε > 0, let uε : Ω → R 2 be a solution of the Ginzburg-Landau system −∆uε = 1 ε 2 uε(1 − |uε| 2) in a Lipschitz bounded domain Ω. In an energy regime that excludes interior vortices, we prove that 1 − |uε| is uniformly estimated by a positive power of ε globally in Ω provided that the energy of uε at the boundary ∂Ω does not grow faster than ε −α with α ∈ (0, 1).

Citation

Ignat, R., Kurzke, M., & Lamy, X. (2020). Global Uniform Estimate for the Modulus of Two-Dimensional Ginzburg-Landau Vortexless Solutions with Asymptotically Infinite Boundary Energy. SIAM Journal on Mathematical Analysis, 52(1), 524-542. https://doi.org/10.1137/19m1262978

• Journal Article Type: Article
• Acceptance Date: Nov 12, 2019
• Online Publication Date: Jan 30, 2020
• Publication Date: 2020-01
• Deposit Date: Nov 19, 2019
• Publicly Available Date: Jan 30, 2020
• Journal: SIAM Journal on Mathematical Analysis
• Print ISSN: 0036-1410
• Electronic ISSN: 1095-7154
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Issue: 1
• Pages: 524-542
• DOI: https://doi.org/10.1137/19m1262978
• Keywords: Applied Mathematics; Analysis; Computational Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/3330620
• Publisher URL: https://epubs.siam.org/doi/10.1137/19M1262978
• Related Public URLs: https://epubs.siam.org/journal/sjmaah
• Contract Date: Nov 19, 2019