| 关于电磁场方程组解的W~(1,p)正则性研究 |
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| 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. |
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| 作者姓名： | 陈志红 李东升 |
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| 作者单位： | 西安交通大学数学与统计学院 西安 710049 |
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| 基金项目： | 国家自然科学基金资助项目（11671316） |
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| 摘 要： | 本文研究了R~3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R~3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
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| 关 键 词： | W~(1 p)正则性 麦克斯韦方程 VMO系数 |
On W1,p Regularity of A System Arising from Electromagnetic Fields |
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| Zhi Hong CHEN,Dong Sheng LI.On W1,p Regularity of A System Arising from Electromagnetic Fields[J].Acta Mathematica Sinica,2019,62(3):381-390. |
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| Authors: | Zhi Hong CHEN Dong Sheng LI |
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| Institution: | School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China |
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| Abstract: | We establish the fundamental W1,p estimate for the weak solution of a system in a bounded domain Ω in R3. The system is related to the steady-state of Maxwell's equations for the magnetic field. The inverse of the principle coefficient matrix is assumed to be in the VMO space. We transform the system to scalar elliptic equations by using the properties of curl and divergence of vector fields in R3. By the regularity theory of elliptic equations, we get the W1,p estimate for 1 < p < ∞. |
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| Keywords: | W1 p regularity Maxwell's equation VMO coefficients |
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