9 papers
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.…
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…
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…