论文标题
平均磁场和应用
Averaging of magnetic fields and applications
论文作者
论文摘要
我们在适当的平面域中估计磁场上适当的平面结构域中的磁性laplacian能量规范。我们的主要贡献是平均估计值，在小细胞中有效，使我们能够从不均匀到均匀的磁场传递。在应用方面，我们得出了在大型磁场强度符合的dirichlet laplacian的最低特征值的新上和下限。此外，我们的平均技术使我们能够估计非线性的金兹堡 - 兰道能量，并且作为副产品，对Dirichlet Magnity Laplacian产生了非高斯试验状态。
We estimate the magnetic Laplacian energy norm in appropriate planar domains under a weak regularity hypothesis on the magnetic field. Our main contribution is an averaging estimate, valid in small cells, allowing us to pass from non-uniform to uniform magnetic fields. As a matter of application, we derive new upper and lower bounds of the lowest eigenvalue of the Dirichlet Laplacian which match in the regime of large magnetic field intensity. Furthermore, our averaging technique allows us to estimate the non-linear Ginzburg-Landau energy, and as a byproduct, yields a non-Gaussian trial state for the Dirichlet magnetic Laplacian.
