电磁散射中边界积分算子的形状导数。第二部分：应用于均匀介质障碍物的散射
Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle
AI总结：
本文通过Helmholtz分解和伪微分算子分析，证明了电磁边界积分算子的无限可微性，并给出了介质散射问题解的一阶形状导数作为新散射问题解的表征。
摘要：
我们发展了有界可穿透障碍物对时谐电磁波散射问题解的形状导数分析。由于边界积分方程是求解电磁散射问题的经典工具，我们研究了标准电磁边界积分算子的形状可微性。后者通常在混合正则性的切向向量场空间 $TH^{-1/2}(\Div_Γ,Γ)$ 上有界。利用Helmholtz分解，我们可以将其分析建立在标准Sobolev空间中伪微分积分算子的研究基础上，但随后需要研究表面微分算子的Gâteaux可微性。我们证明了电磁边界积分算子是无限可微的，且没有正则性损失。我们还给出了介质散射问题解的一阶形状导数作为新电磁散射问题解的表征。
英文摘要：
We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. The latter are typically bounded on the space of tangential vector fields of mixed regularity $TH\sp{-1/2}(\Div_Γ,Γ)$. Using Helmholtz decomposition, we can base their analysis on the study of pseudo-differential integral operators in standard Sobolev spaces, but we then have to study the Gâteaux differentiability of surface differential operators. We prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity. We also give a characterization of the first shape derivative of the solution of the dielectric scattering problem as a solution of a new electromagnetic scattering problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
