Optimal Uniform Elliptic Estimates for the Ginzburg-Landau System

2006/12/09 by S. Fournais, Søren Fournais, Bernard Helffer +3
Computer Science · Mathematics · Physics and Astronomy · #35J60 #35J65 #35Q40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35J60 #msc:35J65 #msc:35Q40

paper · pdf · doi:10.48550/arxiv.math/0612242

20 pages

arxiv created 2006/12/09 · openalex publication_date 2006/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We reconsider the elliptic estimates for magnetic operators in two and three dimensions used in connection with Ginzburg-Landau theory. Furthermore we discuss the so-called blow-up technique in order to obtain optimal estimates in the limiting cases.

Related

• Lorentz Space Estimates for the Ginzburg-Landau Energy
• Averaging of magnetic fields and applications
• The ground state energy of the three dimensional Ginzburg-Landau functional. Part I: Bulk regime
• Large vorticity stable solutions to the Ginzburg-Landau equations
• On approximation of Ginzburg-Landau minimizers by \mathbb S¹-valued maps in domains with vanishingly small holes