外加磁场下Ginzburg-Landau能量的Lorentz空间估计和Jacobian收敛性
Lorentz Space Estimates and Jacobian Convergence for the Ginzburg-Landau Energy with Applied Magnetic Field
摘要：
在本文中，我们继续我们的前一篇文章，\cite{p1}中开始的研究金斯堡-朗道能量的洛伦兹空间估计。我们专注于得到估计的金斯堡-朗道能量与外部磁场$h_{ex}$在某些有趣的制度$h_{ex}$。这使我们能够表明，对于接近能量极小或局部极小的构型，$(u,A)$构型的涡量质量与$\nabla_A u$的$L^{2,\infty}$洛伦兹空间范数相当。我们还建立了规范不变的雅可比（涡度措施）在一个函数空间定义的洛伦兹空间的对偶收敛。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
