5 papers
On the Schiffer and Berenstein conjectures with high-frequency for convex domains in the plane
Guowei Dai, Yingxin Sun, Juncheng Wei +1
In this paper, by introducing two-point stationary-phase amplitude defect, we provide a partial positive answer to the Schiffer and Berenstein conjectures in . More p…
Overdetermined elliptic problems in nontrivial exterior domains of the hyperbolic space
Guowei Dai, Pieralberto Sicbaldi, Yong Zhang
We construct nontrivial unbounded domains in the hyperbolic space , , bifurcating from the complement of a ball, such that the overdetermined ell…
The global bifurcation of periodic internal waves with point vortex and capillary effect
Dai Guowei, Zhang Yong
In this paper, we first construct two-dimensional periodic interface waves with point vortex and capillary effect and then obtain the global structure of the set of solutions. This…
Sign-changing solutions to Schiffer's overdetermined problem on wavy cylinder
Guowei Dai, Yong Zhang
In this paper, we prove the existence of families of smooth unbounded domains with , where \begin{equation} Ω_s=\left\{(x,t)\in \mathbb{R}^…
Interval bifurcation theorems for Fredholm operator and its application to an elliptic overdetermined problem in bounded domains
Guowei Dai, Yong Zhang
We establish local interval bifurcation theorem and global interval bifurcation theorem for Fredholm operator with index via -group. As one of applications, we investigate t…