On The Integrability For The Jacobi Of Orientation-preserving Forms

This paper deals with the integrability of the Jacobian of orientation-preserving forms in anisotropic Sobolev class. By using the classical method of Hadamard's inequality, Hodge decomposition and the results of Riesz transforms, and by the technique of differential forms, singular integrals and the analytical method of Sobolev space, we derive a sufficient condition for the integrability of the Jacobian of orientation-preserving forms.The key points of this paper are:· The results of orientation-preserving mappings are generalized to orientation-preserving forms;· The results of isotropic are generalized to anisotropic;· Utilizing the results of Sobolev space, differential forms, singular integrals, We study the integrability of the Jacobian of orientation-preserving forms in anisotropic Sobolev class.