标题： 稳定骨架积分方程用于一般系数赫尔姆霍兹传输问题 显示英文标题

标题： Stable skeleton integral equations for general coefficient Helmholtz transmission problems

摘要： 一种新的层势和边界积分算子的变分公式通过格林函数推广了它们的经典构造，而格林函数在具有可变系数的赫尔姆霍兹问题中并不显式可用。 波数显式估计和跳跃条件等性质直接来自于其变分定义，并能够对具有分段Lipschitz系数的声学透射问题（TP）进行非局部（“积分”）公式化。 我们直接从底层TP的稳定性中获得积分方程的适定性。 对于一般维度和复波数的同步分析（在本文中）在外部赫尔姆霍兹问题上引入了一个人工边界，并利用了对相关狄利克雷到诺伊曼映射的最新见解。 显示英文摘要

摘要： A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly available for Helmholtz problems with variable coefficients. Wavenumber explicit estimates and properties like jump conditions follow directly from their variational definition and enable a non-local (``integral'') formulation of acoustic transmission problems (TP) with piecewise Lipschitz coefficients. We obtain the well-posedness of the integral equations directly from the stability of the underlying TP. The simultaneous analysis for general dimensions and complex wavenumbers (in this paper) imposes an artificial boundary on the external Helmholtz problem and employs recent insights into the associated Dirichlet-to-Neumann map.