11 papers
A Uniform Pole-Subtracted Limiting Absorption Principle for High-Contrast Elastic Resonator Clusters
Yixian Gao
We establish a uniform pole-subtracted limiting absorption principle for a fixed cluster of \(N\) disjoint three-dimensional high-contrast elastic resonators when the contrast tend…
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…
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…
Lipschitz Stability for an Inverse Problem of Biharmonic Wave Equations with Damping
Minghui Bi, Yixian Gao
We study the recovery of density and initial displacement for a clamped biharmonic wave equation with known damping. For prescribed smooth finite-dimensional coefficient and initia…
Subwavelength resonances in two-dimensional elastic media with high contrast
Yuanchun Ren, Yixian Gao
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lamé parameters and density. Our con…
Construction of Exceptional Points in Time-Modulated High-Contrast Elastic Media
Yixian Gao, Shuguan Ji, Shangling Song
Spatially periodic elastic metamaterials, comprising hard inclusions within a soft matrix in -dimensional space (), exhibit a rich spectrum of physical phenomena. This…
An isoperimetric inequality for lower order Neumann eigenvalues in Gauss space
Yi Gao, Kui Wang
We prove a sharp isoperimetric inequality for the harmonic mean of the first nonzero Neumann eigenvalues for bounded Lipschitz domains symmetric about the origin in Gauss spa…
Limiting absorption principle of Helmholtz equation with sign changing coefficients under periodic structure
Wenjing Zhang, Yu Chen, Yixian Gao
Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complem…
Quantum Birkhoff Normal Form in the -Bruno-Rüssmann non-resonant condition
Huanhuan Yuan, Yixian Gao, Yong Li
The aim of this paper is to construct a Gevrey quantum Birkhoff normal form for the -differential operator where , in the neighborho…