标题： 洛伦兹空间对吉尔伯特-兰道能量的估计 显示英文标题

标题： Lorentz Space Estimates for the Ginzburg-Landau Energy

摘要： 在本文中，我们证明了带有或不带有磁场的Ginzburg-Landau能量的新下界。这些界限依赖于对“涡旋球构造”估计的改进，通过提取能量下界中的一个新正项。这个额外的项可以通过一个Lorentz空间范数进行方便的估计，从而提供一个上界。我们使用的Lorentz空间$L^{2,\infty}$相对于预期的涡旋轮廓是临界的，可以用来估计涡旋的总数并得到改进的收敛结果。 显示英文摘要

摘要： In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space $L^{2,\infty}$ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.