标题： Lorentz空间估计和应用磁场下Ginzburg-Landau能量的雅可比收敛性 显示英文标题

标题： Lorentz Space Estimates and Jacobian Convergence for the Ginzburg-Landau Energy with Applied Magnetic Field

摘要： 在本文中，我们继续研究在我们之前的论文\cite{p1}中开始的Ginzburg-Landau能量的Lorentz空间估计。我们关注在某些有趣的$h_{ex}$范围内，带有外部磁场$h_{ex}$的Ginzburg-Landau能量的估计。这使我们能够证明，对于接近能量的极小值或局部极小值的配置，该配置的漩涡质量$(u,A)$与$\nabla_A u$的$L^{2,\infty}$Lorentz空间范数是可比较的。我们还建立了以Lorentz空间为基准定义的函数空间的对偶空间中的规范不变雅可比行列式（漩涡测度）的收敛性。 显示英文摘要

摘要： In this paper we continue the study of Lorentz space estimates for the Ginzburg-Landau energy started in our previous paper, \cite{p1}. We focus on getting estimates for the Ginzburg-Landau energy with external magnetic field $h_{ex}$ in certain interesting regimes of $h_{ex}$. This allows us to show that for configurations close to minimizers or local minimizers of the energy, the vorticity mass of the configuration $(u,A)$ is comparable to the $L^{2,\infty}$ Lorentz space norm of $\nabla_A u$. We also establish convergence of the gauge-invariant Jacobians (vorticity measures) in the dual of a function space defined in terms of Lorentz spaces.