Variational methods for a singular SPDE yielding the universality of the magnetization ripple
Variational methods for a singular SPDE yielding the universality of the magnetization ripple
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DOI：
10.1002/cpa.22093
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发表时间：
2020-10
影响因子：
3
通讯作者：
R. Ignat;F. Otto;T. Ried;P. Tsatsoulis
中科院分区：
文献类型：
--
作者：
R. Ignat;F. Otto;T. Ried;P. Tsatsoulis
磁化涟漪是在铁磁薄膜中形成的微结构。它可以用非凸能量泛函的最小值来描述，导致由奇异的白色噪声驱动的二维非局部非线性椭圆SPDE。我们使用基于Γ-收敛的变分方法来解决磁化涟漪的普遍特征。由于系统的能量无限大，（随机）能量泛函必须重整化。使用拓扑的Γ-收敛，我们给出了意义的法律的重整化功能，是独立的方式接近白色噪声。更确切地说，这种普遍性在满足谱隙不等式的白色噪声近似类（不一定是高斯）中成立，这使我们能够获得尖锐的随机估计。作为推论，我们得到了最优正则极小解的存在性。
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.