论文标题
通过明确形状的微积分，Helmholtz散射问题的形状可不同性
Shape differentiability of Helmholtz scattering problems via explicit shape calculus
论文作者
论文摘要
我们考虑了Dirichlet，Neumann，阻抗和传播边界条件的时谐标量波散射问题。在这种情况下，我们分析了敏感的衍射场和库奇数据如何对给定标称形状的小扰动。为此，我们遵循[K.。 Eppler，Int。〜J。〜Appl。数学。计算。科学。 10（3）（2000），第487-516页，被称为显式形状微积分，并且非常强调域衍生物作为边界价值问题的表征。它包括结合椭圆规则定理，形状的演算和功能分析，从而推断出域之间的域之间和域之间的尖锐的可区分性结果。该技术适用于经典和限制Sobolev的规律性案例，从而导致新的和全面的可不同性结果。
We consider the time-harmonic scalar wave scattering problems with Dirichlet, Neumann, impedance and transmission boundary conditions. Under this setting, we analyze how sensitive diffracted fields and Cauchy data are to small perturbations of a given nominal shape. To this end, we follow [K. Eppler, Int.~J.~Appl. Math. Comput. Sci. 10(3) (2000), pp. 487-516], referred to as explicit shape calculus, and which places great emphasis on the characterization of the domain derivatives as boundary value problems. It consists in combining elliptic regularity theorems, shape calculus and functional analysis, allowing to deduce sharp differentiability results for the domain-to-solution and domain-to-Cauchy data mappings. The technique is applied to both classic and limit Sobolev regularity cases, leading to new and comprehensive differentiability results.
