论文标题
二维固定$ q $价值的内部规律性
Interior regularity for two-dimensional stationary $Q$-valued maps
论文作者
论文摘要
我们证明，$ 2 $维$ q $ - 价值的地图相对于Dirichlet Energy的外部和内部变化是固定的，这是Hölder的连续，并且其单数集的尺寸最多是一个。在证明过程中，我们为仅相对于外部变化而固定的等效图建立了强浓度 - 纯度定理，并且在每个维度中都有。
We prove that $2$-dimensional $Q$-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions.
