6 papers
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…
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,…
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…
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…
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…
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…