11 papers
A Pole-Subtracted Limiting Absorption Principle for Clusters of High-Contrast Elastic Subwavelength Resonators
Yixian Gao
We establish a pole-subtracted limiting absorption principle for a fixed cluster of \(N\) disjoint three-dimensional high-contrast elastic resonators in the joint regime in which t…
Shape Derivatives for Maxwell's Equations with Nonlinear Boundary Conditions
Chao Deng, Yixian Gao
This paper develops a trace-regular variational framework for time-harmonic Maxwell scattering problems involving pointwise nonlinear boundary and interface responses. We investiga…
Limiting Absorption Principle for the Helmholtz Equation with Sign-Changing Coefficients in Multilayer Spheres
Wenjing Zhang, Yixian Gao
This paper investigates a multilayered Helmholtz model in () characterized by concentric layers of materials with alternating positive and negative refracti…
Lipschitz Stability for an Inverse Problem of Biharmonic Wave Equations with Damping
Minghui Bi, Yixian Gao
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The da…
An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian
Yi Gao, Kui Wang, Anqiang Zhu
In this paper, we investigate a shape optimization problem for the second Robin eigenvalue of the weighted Laplacian on bounded Lipschitz domains symmetric about the origin. Our ma…
Symmetrization of the Maxwell--Neumann--Poincar'e operator, spectral decomposition in traces, and boundary localisation of SPRs
Bochao Chen, Yixian Gao, Hongyu Liu
The Neumann--Poincaré (NP) operator, a fundamental operator in potential theory, has attracted renewed attention for its central role in the analysis of surface plasmon resonances…