Singularities of the quad curl problem
Singularities of the quad curl problem
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DOI：
10.1016/j.jde.2017.12.032
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发表时间：
2018-04
影响因子：
2.4
通讯作者：
S. Nicaise
中科院分区：
文献类型：
--
作者：
S. Nicaise
研究了空间光滑域和非光滑域上的四旋度问题。如果基准是无散度的，我们首先给出一个增广变分公式，等价于[25]的公式。我们描述了变分空间的奇点，这些奇点对应于具有完全传导边界条件的麦克斯韦方程组的奇点。并对光滑数据下相应边值问题解的边奇点和角奇点进行了刻画。最后得到了变分解的一些正则性结果。
We consider the quad curl problem in smooth and non smooth domains of the space. We first give an augmented variational formulation equivalent to the one from [25] if the datum is divergence free. We describe the singularities of the variational space which correspond to the ones of the Maxwell system with perfectly conducting boundary conditions. The edge and corner singularities of the solution of the corresponding boundary value problem with smooth data are also characterized. We finally obtain some regularity results of the variational solution.