关于电磁场方程组解的W1,p正则性研究

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关于电磁场方程组解的W^1,p正则性研究

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关于电磁场方程组解的W^1,p正则性研究陈志红, 李东升西安交通大学数学与统计学院西安 710049 On W^1,p Regularity of A System Arising from Electromagnetic Fields Zhi Hong CHEN, Dong Sheng LISchool of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China

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摘要本文研究了R³中有界区域Ω上的电磁场方程组弱解的W^1，p估计.该方程组来自于磁场所满足的稳态麦克斯韦方程组.在假定系数矩阵的逆属于VMO空间的条件下，利用R³中向量场的旋度和散度的性质，将该方程组转化为标量椭圆型方程组，从而根据椭圆型方程组的正则性理论，得到解的W^1，p估计，其中1 < p < ∞.

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收稿日期: 2018-03-19

MR (2010):

O175.23

基金资助:国家自然科学基金资助项目（11671316）

作者简介: 陈志红,E-mail:zh_chern@163.com;李东升,E-mail:lidsh@mail.xjtu.edu.cn

引用本文:

陈志红, 李东升. 关于电磁场方程组解的W^1,p正则性研究[J]. 数学学报, 2019, 62(3): 381-390. Zhi Hong CHEN, Dong Sheng LI. On W^1,p Regularity of A System Arising from Electromagnetic Fields. Acta Mathematica Sinica, Chinese Series, 2019, 62(3): 381-390.

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[1]	毛安民, 李安然. 薛定谔方程及薛定谔-麦克斯韦方程的多解[J]. Acta Mathematica Sinica, English Series, 2012, 55(3): 425-436.

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