论文标题
Ginzburg-Landau能量具有固定项的振荡速度比连贯长度快
The Ginzburg-Landau energy with a pinning term oscillating faster than the coherence length
论文作者
论文摘要
本文的目的是研究具有振荡固定项的磁性金茨堡 - 兰道功能。我们在这里考虑固定项的振荡速度比连贯长度\（\ varepsilon> 0 \）快得多，这也是Ginzburg-landau参数的倒数。我们研究了周期性潜力的情况和随机固定恒定的情况。我们证明，我们可以将问题的研究减少到固定项，在周期性情况下及其在随机情况下的随机参数方面取代的固定项的情况。为了做到这一点，我们使用了由于lassoued-mironescu引起的能量的脱钩。这使我们研究了带有固定项和均匀的诺伊曼边界条件的金兹堡 - 兰道能量标量阳性最小化器的收敛性。我们证明了这种最小化器通过使用爆炸的论点和liouville型的结果均匀地融合了固定项的平均值，这是由于法利纳（Farina）导致的真实金茨堡-landau/allen-cahn方程的不变解决方案。
The aim of this article is to study the magnetic Ginzburg-Landau functional with an oscillating pinning term. We consider here oscillations of the pinning term that are much faster than the coherence length \(\varepsilon>0\) which is also the inverse of the Ginzburg-Landau parameter. We study both the case of a periodic potential and of a random stationary ergodic one. We prove that we can reduce the study of the problem to the case where the pinning term is replaced by its average, in the periodic case, and by its expectation with respect to the random parameter in the random case. In order to do that we use a decoupling of the energy due to Lassoued-Mironescu. This leads us to the study of the convergence of a scalar positive minimizer of the Ginzburg-Landau energy with pinning term and with homogeneous Neumann boundary conditions. We prove uniform convergence of this minimizer towards the mean value of the pinning term by using a blow-up argument and a Liouville type result for non-vanishing entire solutions of the real Ginzburg-Landau/Allen-Cahn equation, due to Farina.
