Abstract:This paper investigates a multilayered Helmholtz model in $\mathbb{R}^d$ ($d \ge 2$) characterized by concentric layers of materials with alternating positive and negative refractive indices. To overcome the loss of coercivity induced by the sign-changing material parameters, we construct a bespoke $\mathbb T$-coercivity operator to restore the coercive structure of the problem. Furthermore, to address the inherent lack of compactness on unbounded domains, we integrate a complex-wavenumber Dirichlet-to-Neumann (DtN) operator into this framework. By combining this variational synthesis with sharp \textit{a priori} estimates, we rigorously establish the limiting absorption principle and prove the well-posedness of the corresponding transmission problem in appropriate function spaces. Crucially, we quantify the dependence of uniqueness on the domain geometry by explicitly analyzing the optimal trace constant, thereby providing a rigorous mathematical criterion for the design of multi-layer metamaterials.
| Comments: | 27 pages |
| Subjects: | Analysis of PDEs (math.AP) |
| Cite as: | arXiv:2605.24826 [math.AP] |
| (or arXiv:2605.24826v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24826 arXiv-issued DOI via DataCite (pending registration) |
From: Yixian Gao [view email]
[v1]
Sun, 24 May 2026 02:39:29 UTC (89 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。