The Green formula and layer potentials
The Green formula and layer potentials
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格林公式和层势
DOI：
10.1007/bf01295303
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发表时间：
2001
影响因子：
0.8
通讯作者：
R. Duduchava
中科院分区：
文献类型：
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作者：
R. Duduchava
对于一个边值问题，当“基本”算子是具有变矩阵系数的任意偏微分算子，并且“边界”算子是具有向量系数的拟正规算子时，给出了格林公式所有可能变体的显式形式。如果系统存在基本解，则导出解的表示式，并建立相应层势的有界性，将边界上的函数空间(Bessel势、Besov、Zygmund空间)映射到区域上适当的加权函数空间。最后，我们讨论了一些密切相关的问题：来自加权空间的函数迹，势型函数迹，Plemelji公式，Calderón投影，以及曲面和系数的最小光滑性要求。
The explicit form of all possible variants of the Green formula is described for a boundary value problem when the “basic” operator is an arbitrary partial differential operator with variable matrix coefficients and the “boundary” operators are quasi-normal with vector-coefficients. If the system possesses a fundamental solution, a representation formula for the solution is derived and boundedness properties of the relevant layer potentials, mapping function spaces on the boundary (Bessel potential, Besov, Zygmund spaces) into appropriate weighted function spaces on the domain are established. We conclude by discussing some closely related topics: traces of functions from weighted spaces, traces of potential-type functions, Plemelji formulae, Calderón projections, and minimal smoothness requirements for the surface and coefficients.