activity
20242026
collaborators

6 papers

math.AP2026

Mathematical Analysis of Subwavelength Resonances and Gradient Blow-up for Two Close-to-Touching Inclusions within the Two-Dimensional Elasticity

Hongjie Li, Longjuan Xu, Haolun Yang

Subwavelength elastic resonators can concentrate wave energy at length scales far below the incident wavelength, but their behavior becomes especially delicate when two resonators…

math.AP2026

Gradient estimates for the -Laplacian perfect conductivity problem with partially flat and inclusions

Hongjie Dong, Longjuan Xu

In this paper, we investigate the gradient estimates for solutions to the perfect conductivity problem with two closely spaced perfect conductors embedded in a homogeneous matrix,…

math.AP2025

The analysis of resonant frequencies and blow-up estimates of close-to-touching subwavelength resonators in the two-dimensional Helmholtz system

Hongjie Dong, Hongjie Li, Longjuan Xu

In this paper, we investigate wave scattering by a pair of closely spaced inclusions embedded in a homogeneous medium, characterized by a high contrast physical parameters. The sys…

math.AP2025

Gradient continuity estimates for elliptic equations of singular -Laplace type with measure data

Longjuan Xu, Yirui Zhao

In this paper, we are concerned with elliptic equations of -Laplace type with measure data, which is given by w…

math.AP2024

Resonant modes of two hard inclusions within a soft elastic material and their stress estimate

Hongjie Li, Longjuan Xu

In this paper, we are concerned with subwavelength resonant modes of two hard inclusions embedding in soft elastic materials to realize negative materials in elasticity. All the $1…

math.AP2024

Higher order parabolic systems with piecewise DMO and Hölder continuous coefficients

Hongjie Dong, Haigang Li, Longjuan Xu

In this paper, we are concerned with divergence form, higher-order parabolic systems in a cylindrical domain with a finite number of subdomains. We establish and Schaude…