7 citations · 18 across the 21 of their papers we have counts for
23 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 wi…
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…
Estimates for stress concentration between two adjacent rigid inclusions in Stokes flow
Haigang Li, Longjuan Xu
In this paper, we establish the estimates for the gradient and the second-order partial derivatives for the Stokes flow in the presence of two closely located strictly convex inclu…
On higher regularity of Stokes systems with piecewise Hölder continuous coefficients
Hongjie Dong, Haigang Li, Longjuan Xu
In this paper, we consider higher regularity of a weak solution to stationary Stokes systems with variable coefficients. Under the assumptions that coefficients and d…
Stress blow-up analysis when suspending rigid particles approach boundary in 3D Stokes flow
Haigang Li, Longjuan Xu, Peihao Zhang
The stress concentration is a common phenomenon in the study of fluid-solid model. In this paper, we investigate the boundary gradient estimates and the second order derivatives es…
Stress blow-up analysis when a suspending rigid particle approaches the boundary in Stokes flow: 2D case
Haigang Li, Longjuan Xu, Peihao Zhang
It is an interesting and important topic to study the motion of small particles in a viscous liquid in current applied research. In this paper we assume the particles are convex wi…
Higher regularity for solutions to equations arising from composite materials
Hongjie Dong, Longjuan Xu
We consider parabolic systems in divergence form with piecewise coefficients and data in a bounded domain consisting of a finite number of cylindrical subdomains…
Estimates for stress concentration between two adjacent rigid inclusions in two-dimensional Stokes flow
Haigang Li, Longjuan Xu
It is vital important in material sciences and fluid mechanics to study the field enhancements in the narrow region between two inclusions. Complex fluids including particle suspen…
Gradient estimates for Stokes and Navier-Stokes systems with piecewise DMO coefficients
Jongkeun Choi, Hongjie Dong, Longjuan Xu
We study stationary Stokes systems in divergence form with piecewise Dini mean oscillation coefficients and data in a bounded domain containing a finite number of subdomains with $…
Green's function for second order parabolic equations with singular lower order coefficients
Seick Kim, Longjuan Xu
We construct Green's functions for second order parabolic operators of the form in…
Gradient estimates for divergence form parabolic systems
Hongjie Dong, Longjuan Xu
We consider divergence form, second-order strongly parabolic systems in a cylindrical domain with a finite number of subdomains under the assumption that the interfacial boundaries…
Asymptotics of the stress concentration in high-contrast elastic composites
Haigang Li, Longjuan Xu
A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composite with densely packed inclusions whose material prop…
The Optimal Gradient Estimates for Perfect Conductivity Problem with C^{1,α} inclusions
Yu Chen, Haigang Li, Longjuan Xu
In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of v…
Hessian estimates for non-divergence form elliptic equations arising from composite materials
Hongjie Dong, Longjuan Xu
In this paper, we prove that any strong solution to second-order non-divergence form elliptic equations is locally and piecewise when the leading c…
Gradient estimates for divergence form elliptic systems arising from composite material
Hongjie Dong, Longjuan Xu
In this paper, we show that weak solutions to divergence form elliptic systems are Lipschitz and piecewise provided that the leading coefficien…
Characterization of Electric Fields for Perfect Conductivity Problems in 3D
Haigang Li, Fang Wang, Longjuan Xu
In composite materials, the inclusions are frequently spaced very closely. The electric field concentrated in the narrow regions between two adjacent perfectly conducting inclusion…
Estimates for Elliptic Systems in a Narrow Region arising from Composite Materials
Hongjie Ju, Haigang Li, Longjuan Xu
In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general…
Blowup Analysis for the Perfect Conductivity Problem with convex but not strictly convex inclusions
Hongjie Ju, Haigang Li, Longjuan Xu
In the perfect conductivity problem, it is interesting to study whether the electric field can become arbitrarily large or not, in a narrow region between two adjacent perfectly co…
Optimal estimates for the perfect conductivity problem with inclusions close to the boundary
Haigang Li, Longjuan Xu
When a convex perfectly conducting inclusion is closely spaced to the boundary of the matrix domain, a bigger convex domain containing the inclusion, the electric field can be arbi…