10 papers
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,…
Higher derivative estimates for Stokes equations with closely spaced rigid inclusions in three dimensions
Hongjie Dong, Haigang Li, Huaijun Teng +1
In this paper, we establish higher-order derivative estimates for the Stokes equations in a three-dimensional domain containing two closely spaced rigid inclusions. We construct a…
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…
Optimal gradient estimates for conductivity problems with imperfect low-conductivity interfaces
Hongjie Dong, Haigang Li, Yan Zhao
This paper studies field concentration between two nearly touching conductors separated by imperfect low-conductivity interfaces, modeled by Robin boundary conditions. It is known…
Serrin's overdetermined theorem within Lipschitz domains
Hongjie Dong, Yi Ru-Ya Zhang
Let be a Lipschitz domain. We prove that, satisfies the following Serrin-type overdetermined system $$u \in W^{1,2}(\mathbb R^n), \quad u=0\ \text{ a.e. i…
Optimal higher derivative estimates for Stokes equations with closely spaced rigid inclusions
Hongjie Dong, Haigang Li, Huaijun Teng +1
In this paper, we study the interaction between two closely spaced rigid inclusions suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narr…
Optimal higher derivative estimates for solutions of the Lamé system with closely spaced hard inclusions
Hongjie Dong, Haigang Li, Huaijun Teng +1
We investigate higher derivative estimates for the Lamé system with hard inclusions embedded in a bounded domain in . As the distance between two clos…
Global BMO-Sobolev Estimates for Second-Order Linear Elliptic Equations on Lipschitz Domains
Hongjie Dong, Dachun Yang, Sibei Yang
Let and be a bounded Lipschitz domain. In this article, we establish first-order global regularity estimates in the scale of BMO spaces on for…
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…
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…