磁场作用下$H_{c_1}$附近层状超导体Lawrence-Doniach能的收敛
Convergence of the Lawrence-Doniach Energy for Layered Superconductors with Magnetic Fields near $H_{c_1}$
摘要：
我们分析了三维层状结构高各向异性超导体的Lawrence-Doniach能量极小化。对于这样一个超导体占据一个有界的广义圆柱体的$\mathbb{R}^3$与等距平行层，我们假设一个施加的磁场是垂直于层的强度$h_{ex}\sim|\lnε|$为$ε\rightarrow 0$，其中$ε$是金斯堡-朗道参数的倒数。我们证明了能量最小化的各种物理量的紧性结果，并推导出Lawrence-Doniach能量的伽玛极限为$ε$，层间距离$s$趋于零，在附加的假设下，层是弱耦合的（即，$s\ggε$）。
英文摘要：
We analyze minimizers of the Lawrence-Doniach energy for three-dimensional highly anisotropic superconductors with layered structure. For such a superconductor occupying a bounded generalized cylinder in $\mathbb{R}^3$ with equally spaced parallel layers, we assume an applied magnetic field that is perpendicular to the layers with intensity $h_{ex}\sim|\lnε|$ as $ε\rightarrow 0$, where $ε$ is the reciprocal of the Ginzburg-Landau parameter. We prove compactness results for various physical quantities of energy minimizers, and derive a Gamma-limit of the Lawrence-Doniach energy as $ε$ and the interlayer distance $s$ tend to zero, under the additional assumption that the layers are weakly coupled (i.e., $s\ggε$).
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