It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is co...It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is complexity,the Jacobian determinant included in the kernel is expanded for making clearly the expression of the kernel.Moreover,one differential operator is utilized for setting up relations between integrals with higher and usual orders.The work also concerns the convergent properties of the integral.In order to study Hadamard principal value and composite formula of this integral,finite and divergent parts will be estimated and separated.As an application,solvability of the system of integral equations with higher order singularity kernel is discussed.展开更多
In this paper, the first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a certain system of singular ...In this paper, the first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a certain system of singular integral equations with several undetermined constants, which is proved to be uniquely solvable when these constants are suitably and uniquely chosen.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11771357)。
文摘It is known that principal value plays vital roles in the study of singular integral.In this paper,one type of Cauchy–Fantappièintegral with multiple indexes is introduced.Since the structure of the kernel is complexity,the Jacobian determinant included in the kernel is expanded for making clearly the expression of the kernel.Moreover,one differential operator is utilized for setting up relations between integrals with higher and usual orders.The work also concerns the convergent properties of the integral.In order to study Hadamard principal value and composite formula of this integral,finite and divergent parts will be estimated and separated.As an application,solvability of the system of integral equations with higher order singularity kernel is discussed.
文摘In this paper, the first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a certain system of singular integral equations with several undetermined constants, which is proved to be uniquely solvable when these constants are suitably and uniquely chosen.
