On Representation Formulas and Radiation Conditions
On Representation Formulas and Radiation Conditions
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DOI：
10.1002/(sici)1099-1476(19970125)20:2
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发表时间：
1997-01
影响因子：
2.9
通讯作者：
M. Costabel;M. Dauge
中科院分区：
文献类型：
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作者：
M. Costabel;M. Dauge
无界区域上的线性椭圆型偏微分方程的解，如果在无穷远处满足一定的条件，则可用边界势来表示。这些辐射条件取决于为积分表示选择的基本解。我们在一个相当一般的框架下证明了一些关于辐射条件的基本结果。基本解G被认为是只定义在一个紧集的补。事实证明，然而，我们提出的例子，更有趣的结果，只有当G是定义在所有的R或如果它是一个绿色函数的外部边界值问题。
Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework. Fundamental solutions G are considered that are defined only on the complement of a compact set. It turns out, however, and we present examples for this, that the more interesting results only hold if G is defined on all of R or if it is a Green function for an exterior boundary value problem.