论文标题
PFAFF系统的最佳规律性和等距浸入任意维度
Optimal regularity for the Pfaff system and isometric immersions in arbitrary dimensions
论文作者
论文摘要
我们证明存在，唯一性和$ w^{1,2} $ - 针对PFAFF系统的解决方案，具有反对称$ l^2 $ ceefficited矩阵，以任意维度为单位。因此，我们在$ w^{2,2} $ - 等距沉浸液的存在与高斯 - codazzi-ricci方程的弱溶解度之间建立了等效性。这些结果的规律性假设很敏锐。作为一个应用程序，我们针对$ w^{2,2} _ {\ rm loc} $ - 浸入$ W^{2,2} _浸入。
We prove the existence, uniqueness, and $W^{1,2}$-regularity for the solution to the Pfaff system with antisymmetric $L^2$-coefficient matrix in arbitrary dimensions. Hence, we establish the equivalence between the existence of $W^{2,2}$-isometric immersions and the weak solubility of the Gauss--Codazzi--Ricci equations on simply-connected domains. The regularity assumptions of these results are sharp. As an application, we deduce a weak compactness theorem for $W^{2,2}_{\rm loc}$-immersions.
