Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C 2 are extended to the Lipschitz case. In particular, this yields an elementary way to establish the mapping properties of elastic wave potentials from those of the scalar Helmholtz equation without resorting to the more advanced theory for elliptic systems in the Lipschitz domains. Scalar Günter derivatives of a function defined on the boundary of a three-dimensional domain are expressed as components (or their opposites) of the tangential vector rotational ∇ ∂Ω u × n of this function in the canonical orthonormal basis of the ambient space. This, in particular, implies that these derivatives define bounded operators from H s to H s−1 (0 ≤ s ≤ 1) on the boundary of the Lipschitz domain and can easily be implemented in boundary element codes. Representations of the Guünter operator and potentials of single and double layers of elastic waves in the two-dimensional case are provided.

中文翻译：

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将 Günter 导数扩展到 Lipschitz 域以及在弹性波的边界势中的应用

先前为 C 2 类域构建的弹性波势的跟踪和牵引的正则化技术扩展到 Lipschitz 情况。特别是，这产生了一种基本方法，可以根据标量亥姆霍兹方程的那些来建立弹性波势的映射特性，而无需求助于 Lipschitz 域中椭圆系统的更高级理论。定义在三维域边界上的函数的标量 Günter 导数表示为该函数在环境空间的规范正交基中的切向矢量旋转 ∇ ∂Ω u × n 的分量（或它们的对立面）。这，特别是，意味着这些导数在 Lipschitz 域的边界上定义了从 H s 到 H s−1 (0 ≤ s ≤ 1) 的有界算子，并且可以很容易地在边界元代码中实现。提供了在二维情况下 Guünter 算子的表示以及单层和双层弹性波的势能。