论文标题
奇异SPDE的变化方法产生了磁化涟漪的普遍性
Variational methods for a singular SPDE yielding the universality of the magnetization ripple
论文作者
论文摘要
磁化涟漪是在薄铁磁膜中形成的微观结构。它可以通过非凸能功能的最小化来描述，从而导致非本地和非线性椭圆形SPDE在由白噪声驱动的两个维度上，这是单数。我们使用基于$γ$ -Convergence的变分方法来解决磁化纹波的通用特征。由于系统的无限能量，必须将（随机）能量功能重新归一化。使用$γ$ - 融合的拓扑结构，我们了解了重新归一化功能的定律，该定律与白噪声的方式无关。更确切地说，这种普遍性在满足光谱间隙不等式的白噪声（不一定是高斯）近似的类别中，这使我们能够获得尖锐的随机估计值。作为推论，我们获得了具有最佳规律性的最小化器的存在。
The magnetization ripple is a microstructure formed in thin ferromagnetic films. It can be described by minimizers of a nonconvex energy functional leading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by white noise, which is singular. We address the universal character of the magnetization ripple using variational methods based on $Γ$-convergence. Due to the infinite energy of the system, the (random) energy functional has to be renormalized. Using the topology of $Γ$-convergence, we give a sense to the law of the renormalized functional that is independent of the way white noise is approximated. More precisely, this universality holds in the class of (not necessarily Gaussian) approximations to white noise satisfying the spectral gap inequality, which allows us to obtain sharp stochastic estimates. As a corollary, we obtain the existence of minimizers with optimal regularity.
