We consider the Helmholtz problem with source term in an anisotropic domain of ${\mathbb{R}}^3$. The aim of this paper is to investigate the interplay between the geometry and analysis of elliptic equations under small perturbation of domain. The solving of this problem, anisotropic as well as isotropic case, is based on integral equations. We exhibit the Lippmann-Schwinger integral equation in the presence of finite number of anisotropic inclusions of small diameter. We derive some results for convergence estimates.

中文翻译：

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小各向异性夹杂物存在下亥姆霍兹问题的积分方程方法

我们在各向异性域中考虑具有源项的亥姆霍兹问题${\mathbb{R}}^3$. 本文的目的是研究在域的小扰动下椭圆方程的几何与分析之间的相互作用。这个问题的解决，各向异性以及各向同性的情况，是基于积分方程。我们在存在有限数量的小直径各向异性夹杂物的情况下展示了 Lippmann-Schwinger 积分方程。我们得出了一些收敛估计的结果。