中文摘要：

空间映射的Jacobi行列式是研究高维空间几何函数论与非线性分析的有力工具。高维空间映射的可积性研究往往归结于Jacobi行列式可积性的研究。研究各向异性条件下的空间映射Jacobi行列式的子式,利用Stokes公式和Sobolev空间的分析技巧,建立了一个与空间映射的子式有关的估计式,推广了Iwaniec,Martin等人的结果。这个估计式对高维空间映射可积性的研究具有一定的意义。

英文摘要：

The Jacobian Determinants of space mappings are effective tools in the study of geometric funcion theory in high - dimensional spaces and nonlinear analysis. The study of integrability of mappings in high - dimensional spaces is often attributed to the study of the integrability of Jacobian determinants. The minors of the Jacobian determinants of mappings in anisotropic Sobolev spaces is studied. An estimate related to the minors of space maps is established by using Stokes＇ formula and the analytic technique of Sobolev spaces, which generalizes a known result due to Iwaniec and Martin. This estimate is useful to the study of the integrability of space mappings.