【作者】 朱江红；

【导师】 高红亚；

【作者基本信息】 河北大学 ， 基础数学， 2004， 硕士

【摘要】 高阶奇异积分在物理学和工程技术中有广泛的应用。奇点位于区域内部的高整数阶奇异积分和奇点位于区域边界的高整数阶和高分数阶奇异积分已经被研究。本文考虑奇点位于区域内部的二维高分数阶奇异积分。利用Hadamard关于发散积分的有限部分的思想,给出了其Hadamard主值的表达式,并得到其可微性性质。更多还原

【Abstract】 Singular integrals of high order have wide applications in many fields, such as physics and engineering. The singular integrals of high integral order when the singularities lie in the interior of the domain, the singular integrals of high integral and fractional order have been studied. This paper considers two dimensional sigular integrals of higher fractional order with the sigularity lies in the interior of the domain. The formula of the Hadamard principal value is obtained by using the idea of Hadamard on the "finite part" of divergent integral, and the differentbility property of it is derived.更多还原