与Time-harmonic Maxwell方程有关的Cauchy型积分算子的性质  

Some properties of the Cauchy-type integral operators associated with the time-harmonic Maxwell equations

作　　者：高龙 王丽萍[1] 贾珊珊 罗利萍 邱芬 GAO Long;WANG Li-ping;JIA Shan-shan;LUO Li-ping;QIU Fen(School of Mathematical Science,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024

出　　处：《高校应用数学学报（A辑）》2021年第3期349-363,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：河北省自然科学基金(A2020205008,A2015205012);河北师范大学重点基金(L2021Z01);国家自然科学基金(11401162,11871191,11571089)。

摘　　要：首先介绍了与N算子有关的Cauchy型积分算子,并证明了以下三种情况下的Holder连续性:两点在边界上;一点在边界上,另一个在区域内(在区域外);两点在区域内(在区域外).接下来介绍了与Time-harmonic Maxwell方程有关的Cauchy型积分算子,研究了它与N矩阵算子有关的Cauchy型积分算子的关系.最后利用上述关系,给出了与Time-harmonic Maxwell方程有关的Cauchy型积分算子在上述三种情况下的Holder连续性.In the first place,the Cauchy-type integral operator related to the N matrix operator is introduced.And the Holder continuity is proved in the following three cases:two points are on the boundary;one is on the boundary and the other is inside the region(outside the region);two points are inside the region(outside the region)respectively.Then the Cauchy-type integral operator related to the Time-harmonic Maxwell equations is introduced,and the relationship between it and the Cauchy-type integral operator related to the N matrix operator is also studied.Finally,by using of their relationship,the Holder continuity of the Cauchy-type integral operator related to the Time-harmonic Maxwell equation under the above three cases are also given respectively.

关 键 词：HOLDER连续 Cauchy型积分算子 N矩阵算子 Time-harmonic Maxwell方程 

分 类 号：O174.5[理学—数学]